Compact single-aperture antenna and direction-finding navigation system

ABSTRACT

A radio-based navigation system uses a small multi-mode direction-finding antenna and a direction-finding receiver to determine platform position, velocity, attitude and time while simultaneously providing protection against narrowband and broadband sources of interference. Global Navigation Satellite System (GNSS) signals such as those from a Global Positioning System (GPS) provide attitude measurements with a compact multi-mode direction-finding antenna (e.g., a small two-arm spiral with improved angle-of-arrival performance over the entire hemisphere enhanced through use of a conductive vertical extension of the antenna ground plane about the antenna perimeter and/or conductive posts placed evenly around the antenna perimeter) that provides protection against jammers. The multi-mode spiral may be treated as an array of rotationally-symmetric antenna elements. The GPS receiver architecture may be modified for direction-finding and thereby attitude determination by increasing the number of input signals from one to at least two while minimizing the required number of correlators and mixers.

RELATED APPLICATIONS

This non-provisional application is a division of commonly assigned U.S.application Ser. No. 12/457,512 filed on Jun. 12, 2009, naming KenanEzal, Tariq Mujahed and Ben Werner as co-inventors, which is acontinuation-in-part of U.S. application Ser. No. 12/155,102 filed onMay 29, 2008 (now abandoned), which further claims priority rights basedon U.S. Provisional Application Ser. No. 60/924,727 filed on May 29,2007. Application Ser. Nos. 12/457,512, 12/155,102 and 60/924,727 arehereby incorporated by reference. This application is also related tocommonly assigned U.S. Pat. No. 7,577,464 issued on Aug. 18, 2009.

BACKGROUND OF THE INVENTION 1. Technical Field

In general the present application relates to the field of antennas andradio-based navigation systems. Specifically, it relates to multi-modedirection-finding (DF) antennas; radio-based navigation receivers foruse with a global navigation satellite system (GNSS) such as the GlobalPositioning System (GPS), GALILEO, and GLONASS; as well as the fields ofradio-frequency (RF) interference rejection, RF direction finding, andradio-based attitude determination.

2. List of References

U.S. Patents 3,144,648 August 1964 Dollinger 342/365 4,366,483 December1982 Hagedon et al. 343/113 R 4,591,862 May 1986 Parkhurst et al.343/427 4,630,064 December 1986 Andrews et al. 343/895 5,173,700December 1992 Chesley 342/17 5,185,610 February 1993 Ward et al. 342/3575,313,216 May 1994 Wang et al. 343/700 MS 5,327,143 July 1994 Goetz etal. 342/382 5,461,387 October 1995 Weaver 342/357 5,621,422 April 1997Wang 343/895 5,940,026 August 1999 Popeck 342/357.01 6,281,841B1 August2001 Nevill 342/424 6,452,543B1 September 2002 Tseng et al 342/357.116,520,448B1 February 2003 Doty et al. 244/3.23 6,580,389B2 June 2003Speyeret al. 342/357.11 6,598,009B2 July 2003 Yang 702/152 6,876,337B2April 2005 Larr 343/818 7,577,464B2 August 2009 Ezal et al 455/562.1

U.S. Patent Applications 11/154,952 June 2005 Ezal et al (now 455/562.1U.S. Pat. No. 7,577,464) 12/155,102 May 2008 Ezal et al (now abandoned)342/357.12

Books

-   S. Blackman and R. Popoli, Design and Analysis of Modern Tracking    Systems, Artech House, Boston, Mass., 1999.-   C. E. Cohen, “Attitude Determination,” in Global Positioning System:    Theory and Applications, Volume II, B. Parkinson and J. J. Spilker,    Jr., editors, Washington, D.C., American Institute of Astronautics    and Aeronautics, 1996.-   R. T. Compton, Adaptive Antennas: Concepts and Performance, 1988.-   R. G. Corzine and J. A. Mosko, Four-arm Spiral Antennas, Artech    House, 1990.-   R. N. Ghose, Interference Mitigation: Theory and Application, IEEE    Press, 1996.-   E. D. Kaplan and C. Hegarty (Editors), Understanding GPS: Principles    and Applications, Second Edition, 2005.-   H. D. Kennedy and W. Wharton, “Direction-Finding Antennas and    Systems,” Antenna Engineering Handbook, Second Edition, R. C.    Johnson and H. Jasik, editors, Chapter 39, 1984.-   S. E. Lipsky, Microwave Passive Direction-finding, John Wiley &    Sons, 1987.-   B. W. Parkinson and J. J. Spilker (Editors), Global Positioning    System: Theory & Applications, Volumes I and II, 1996.

Articles

-   P. Axelrad and C. P. Behre, “Satellite Attitude Determination Based    on GPS Signal-to-Noise Ratio,” Proceedings of the IEEE, vol. 87, no.    1, pp. 133-144, January 1999.-   L. G. Bullock, et al., “An Analysis of Wide-Band Microwave Monopulse    Direction-Finding Techniques,” IEEE Transactions on Aerospace and    Electronic Systems, vol. 7, no. 1, pp. 188-203, January 1971.-   G. A. Deschamps and J. D. Dyson, “The Logarithmic Spiral in a    Single-Aperture Multimode Antenna System,” IEEE Transactions on    Antennas and Propagation, vol. 19, no. 1, pp. 90-96, January 1971.-   K. Ezal and C. Agate, “Tracking and interception of ground-based RF    sources using autonomous guided munitions with passive bearings-only    sensors and tracking algorithms,” Proceedings of the SPIE, April    2004.-   J. Farrell and J. Stuelpnagel, “Solution to ‘A Least Squares    Estimate of Satellite Attitude,’” SIAM Review, vol. 8, no. 3, pp.    384-386, 1966.-   W. Grossman, “Bearings-Only Tracking: A Hybrid Coordinate System    Approach,” Proceedings of the Conference on Decision and Control,    pp. 2032-2037, 1991.-   J. Huang, “Circularly Polarized Conical Patterns from Circular    Microstrip Antennas,” IEEE Transactions on Antennas and Propagation,    pp. 991-994, vol. 32, no. 9, September 1984.-   J. A. Mosko, “An Introduction to Wideband Two-Channel    Direction-Finding Systems, Parts I and II,” Microwave Journal,    February & March 1984.-   H. Nakano, et al., “A Spiral Antenna Backed by a Conducting Plane    Reflector,” IEEE Transactions on Antennas and Propagation, vol. 34,    no. 6, June 1986.-   R. P. Penna and K. M. Pasala, “Theory of Angle Estimation Using    Multiarm Spiral Antenna,” IEEE Transactions on Aerospace and    Electronic Systems, vol. 37, no, 1, January 2001.-   R. P. Penno, K. M. Pasala, and S. Schneider, “Mitigation of Jamming    of an Angle Estimation System Using Multi-mode Antennas,”    Proceedings of the IEEE Aerospace Conference, vol. 2, pp. 833-839,    2002.-   M. L. Psiaki, “Attitude Sensing Using a Global-Positioning-System    Antenna on a Turntable,” Journal of Guidance, Control, and Dynamics,    vol. 24, no. 3, pp. 474-481, May-June 2001.-   G. Wahba, “A Least Squares Estimate of Satellite Attitude,” SIAM    Review, vol. 7, no. 3, p. 409, July 1965.-   J. J. H. Wang and V. K. Tripp, “Design of Multioctave Spiral-Mode    Microstrip Antennas,” IEEE Transactions on Antennas and Propagation,    vol. 39, no. 3, March 1991.-   J. J. H. Wang, J. K. Tillery, and M. A. Acree, “Multioctave Wideband    Mode-0 Operation of Spiral-Mode Microstrip Antennas,” Proceedings of    the Antennas and Propagation Society International Symposium, vol.    3, pp. 1860-1863, July 1997.-   J. J. H. Wang, “Theory of a Class of Planar Frequency-Independent    Omnidirectional Traveling-Wave Antennas,” Proceedings of the IEEE    International Symposium on Microwave, Antenna, Propagation and EMC    Technologies for Wireless Communications, p. 434, 2005.

Standards

-   IEEE Standards Board, IEEE Standard Definitions of Terms for    Antennas, IEEE Standard 145, 1993.

3. Related Art

Numerous civilian and military applications have been developed based onsatellite navigation systems and an increasing number of systems rely onthe navigational accuracy provided by GPS. Other examples of satellitenavigation systems include Europe's GALILEO and Russia's GLONASS, aswell as systems currently being developed by other nations includingIndia, China and Japan. Under these radio-based navigation systems, amultitude of satellites orbiting earth send out coded signals containinginformation regarding the satellite trajectories (ephemeris) and time(almanac). Each satellite signal waveform is assigned a unique code orfrequency that is known a priori by the receiving platform. Militaryversions of these signals are encrypted so that only those receiverswith appropriate decryption equipment can decipher the satellitesignals. Receiver position, velocity and time (PVT) are determined fromthe measured time-of-flight, or pseudo-range of four or more satellitesignals and the known positions of those satellites. The propertechniques and methods for receiving and processing of satellite signalsto obtain own-platform position, velocity and time are well known: See,for example, Kaplan and Hegarty (2005) and Parkinson and Spilker (1996).

It is generally recognized that the performance of GPS is greatlyenhanced when it is coupled with an inertial navigation system (INS). InGPS/INS systems, the low-frequency position and velocity measurementsprovided by GPS help calibrate and reduce the bias and scale factorerrors of inertial measurement units (IMUs). The IMUs providehigh-frequency measurements that bridge the gap between successivelow-frequency GPS measurements. In return, the INS aids in theacquisition and tracking of GPS satellites by allowing a reduction inthe GPS receiver carrier- and code-tracking loop bandwidths. Reducingthe loop bandwidth decreases the noise (as well as the jamming power)and increases the satellite signal-to-interference-plus-noise ratio(SINR).

Many platforms place severe constraints on the size, weight and power(SWAP) of onboard sensors and electronics, making it very difficult tobuild navigation systems that are capable of providing the neededaccuracy while meeting the SWAP constraints. While micro-electricalmechanical systems (MEMS) have reduced the size and weight of sensorsused for inertial navigation, the reduction in size has also resulted ina decrease in performance, especially when considering low-cost MEMSgyros. In contrast to tactical-grade gyros that have rate biases on theorder of one degree per hour, MEMS gyros have rate biases of hundreds ofdegrees per hour and their performance tends to be highlytemperature-sensitive. Without GPS, these large biases translate intolarge growths in error over short periods of time. Hence, it isimportant to augment MEMS IMUs with alternative sensors that improve thenavigation performance and specifically the attitude accuracy withoutsignificantly adding to the overall cost, volume, weight and powerconsumption of the system.

Since satellite-based navigation systems typically require three or moreantennas (multiple apertures) separated at least 0.5 meters apart(greater than two wavelengths) to obtain 3-D attitude measurements [U.S.Pat. No. 5,185,610 and Cohen 1996], most GPS/INS systems rely on the IMUto provide attitude measurements. GPS-based attitude (GPS/A) is computedfrom the estimated platform position, the known satellite positions, andthe measured angle-of-arrival (AOA) of each satellite signal. Theadvantage of GPS-based attitude sensors is that they are relativelytemperature insensitive and have no known drift mechanism inmultipath-free environments. Multi-element, multi-aperture GPS/A systemswith large baselines (D) between each element, where D>λ and λ is thelowest wavelength of interest, determine the AOA via phaseinterferometry. Phase interferometry relates to measuring the phase/timedifference of arrival of the same signal received by two different anddistinct antenna elements (apertures). However, most small platformscannot accommodate large baselines or more than one GPS antenna.Platform attitude for a single-axis can be determined with asingle-aperture non-spinning antenna from calibrated satellitesignal-to-noise ratios [Axelrad 1999]. Alternative single-apertureattitude systems require the antenna to be spinning at a known rate[Psiaki 2001] or traveling with a non-zero velocity [U.S. Pat. No.6,580,389 B2]. A novel GPS/A sensor described in U.S. Pat. No. 5,461,387requires a single-aperture multi-mode direction-finding antenna withthree or more arms (elements) and an analog mode-forming networkcomprising phase shifters and hybrid combiners, but does not providesimultaneous anti-jam GPS capability.

Attitude estimation is especially challenging for spinning platformssuch as spin-stabilized munitions and spacecraft primarily becauseexisting low-cost gyroscope technology has difficulty in trackingrotation rates in excess of 360°/s (1 Hz). In general, smallspin-stabilized munitions and space vehicles cannot supportlarge-baseline multi-aperture GPS/A systems. Such systems are usuallylimited to a maximum dimension of less than 5 inches or less thanseven-tenths of one GPS signal wavelength (D<0.7λ). In addition,existing GPS/A antenna systems for spinning platforms (such asmunitions) are only able to measure the roll angle using GPS, but notthe yaw or pitch [Doty 2003]. These systems rely on the modulation ofthe received signal due to the rotation to track the spin rate and rollangle, and are incapable of determining the roll angle for non-spinningplatforms. Furthermore, due to an increase in the relative phase noise,multi-aperture phase interferometric systems do not work well when theantenna elements are in such close proximity. In contrast tophase-interferometry systems, the AOA and attitude accuracy of single-and multi-aperture monopulse DF systems rely on the purity of the DFantenna modes (lobes), not on the baseline length.

The AOA of an RF signal can be obtained through either monopulse orsequential direction-finding systems that are either active or passive;the use of interferometric systems; or adaptive array processingtechniques, which are computationally very expensive. Adirection-finding system comprises one or more antennas or antennaelements and a receiver such that the azimuth and/or the elevation angleof an incoming signal can be determined. Direction-finding systems useeither scalar or vector processing to determine the AOA of a signal.Scalar systems work with either the amplitude or phase of a signal,while vector systems work with both amplitude and phase. The receiver ofa DF system can be either monopulse or sequential and may have one ormore RF channels. Monopulse DF is also referred to as simultaneouslobing or simultaneous lobe (mode) comparison. Single-channel systems,such as that of U.S. Pat. No. 5,461,387, either use a rotating antennaelement or sequentially switch between two or more antenna outputs. Ingeneral, however, AOA information is obtained by comparing the amplitudeand/or the phase of two or more RF channels (modes/lobes).Amplitude-comparison systems measure the relative amplitude of two ormore channels to determine the AOA, while phase-comparison systemsmeasure the relative phase between channels. Monopulseamplitude-comparison systems usually rely on beam- or pattern-formingnetworks that generate at least two beams (lobes) from at least two DFmodes to obtain AOA measurements. Single-aperture spiral antennas arewell known for their two-channel DF capability [Deschamps 1971].Single-element circular patch antennas have also been shown to becapable of supporting two or more direction-finding modes [Huang 1984].

Hybrid systems that measure both relative amplitude and phase arereferred to as amplitude-phase-comparison systems. The comparison takesplace either simultaneously (monopulse), or sequentially. Monopulse(simultaneous lobe comparison) systems are more robust because theyeliminate the effects of emitter phase and amplitude variations as afunction of time and are less susceptible to electronic counter measures(ECM). Depending on the application, DF systems measure either theelevation (θ) or azimuth (φ) angle-of-arrival, or both. A detailedanalysis of DF systems can be found in Bullock (1971), Kennedy (1984)and Lipsky (1987).

The location of an emitter is generally determined by triangulation ofsimultaneous (or near-simultaneous) AOA measurements from multiple DFsystems that are spatially diverse, or through multiple AOA measurementsfrom a moving DF system [Grossman 1991, Blackman 1999, Ezal 2004]. Inorder to determine the location of an emitter it is also necessary toknow the position of the DF sensor for each AOA measurement. ForGPS-based attitude systems, the emitter (satellite) locations areobtained through standard processing of the GPS signal that contains anavigation message with satellite ephemeris and almanac information[Kaplan 2005, Parkinson 1996].

Unfortunately, intentional and unintentional interference are commonproblems in the field of wireless communications, and GPS is noexception. When the desired signal arrives along a reflected path, ittoo can behave like an interference signal. This is often referred to asmultipath or coherent interference, which can lead to partialcancellation of the signal strength and result in signal fade ordropout. Signals unrelated to the desired signal are referred to asincoherent interference and can be either broadband or narrowband. Inthe case of digital communications, both coherent and incoherentinterference can lead to unacceptable bit error rates (BERs), loss ofsignal lock, or a corruption of the information or message in thedesired signal.

The most common methods of interference rejection are beam steering,null steering, signal cancellation, polarization filtering, frequencyincision, tapped-delay lines, and adaptive signal processing [Compton1988, Ghose 1996]. Most of these techniques require multi-elementmulti-aperture antennas or phased arrays to successfully eliminateinterfering signals. Array-based systems are capable of providing bothinterference rejection and the AOA of the interfering signals.Interference suppression in conventional adaptive array systems isachieved by summing the complex weighted outputs from two or moreantenna elements. A processor determines a complex weight or set ofweights for each output signal. If the weights are chosen correctly, theeffective power of the interference in the final output will besignificantly reduced and the desired signal strength will be enhanced.This approach to interference mitigation is performed solely within anelectronic package that has two or more antenna input ports. Each suchport is connected to an antenna element via an RF (radio- orcarrier-frequency) transmission line of some type. The antenna elementsare designed to have coverage that is as broad as possible, but areoffset from each other in position and/or orientation. These offsetshave to be large enough so that there are sufficient signal phasedifferences among the individual element outputs. The processor usesthese phase differences to advantage in determining the appropriateweights. For adequate spatial filtering, element separations rangingfrom 0.3 to 0.5 carrier wavelengths are required, which is often toolarge for many small platforms. A good description of interferencemitigation techniques can be found in Ghose 1996.

Although there are numerous GPS receiver systems, with and withoutGPS-based attitude, and with and without anti-jam capabilities, there isno single navigation system that provides GPS-based position andvelocity, AJ GPS, GPS-based attitude measurements, and direction-findingcapability in a small form-factor with a single-aperture multi-modeantenna. For example, U.S. Pat. No. 5,461,387 describes a singleaperture GPS-based position and direction-finding instrument that isunable to provide anti-jam GPS protection. Moreover, it requires ananalog mode-forming feed network, and the use of Modes 1 and 2 of adirection-finding multi-mode antenna with at least three arms. Mode 2 ofa spiral with three or more arms requires the circumference of theantenna to be at least two wavelengths [Mosko 1984]. Since the L1 GPSwavelength (λ) in air is approximately 19 cm, the antenna aperture needsto be at least 115 cm² and requires a minimum diameter of 12.1 cm(0.64λ), which is far too large for many applications. In practice, thefour-arm spiral diameter needs to be approximately 15 cm (˜0.78λ) toefficiently support Mode 2. One possible solution to this problem is touse a two-arm spiral, which does not require as large an aperture.However, it has long been believed that direction-finding is notpractical with two-arm spirals. For example, U.S. Pat. No. 4,630,064states that “a two-arm spiral antenna is impractical for direction ofarrival sensing and multipolar operation” [Andrews et al, column 1, line65].

There are at least two traditional reasons against the use of two-armspirals for direction-finding. First, Mode 0 is difficult to excite.Second, the mode patterns of spirals with three or more arms have tendedto be more symmetric and, therefore, more accurate for direction-findingapplications than two-arm spirals. This is because currentsingle-aperture n-mode direction-finding antennas, such as spirals, haven-fold cylindrical (rotational) symmetry, which significantly limitstheir useful operating range to less than 60° about their boresight, or50% of a hemisphere, and in most cases to less than 30° about theirboresight, or only 13.4% of a hemisphere. For example, a four-arm spiralantenna has four-fold cylindrical (rotational) symmetry and, hence, thecomplex gain pattern repeats four times about its boresight. This makesit difficult to uniquely identify the angle-of-arrival frommeasurements.

In contrast to U.S. Pat. No. 5,461,387, U.S. Pat. No. 7,577,464describes a single-aperture anti-jam GPS antenna system withdirection-finding capability. However, although the system described byU.S. Pat. No. 7,577,464 does have DF capability from which GPS-basedattitude measurements can be obtained, the system is unable to provideanti-jam GPS protection while simultaneously obtaining GPS-basedattitude measurements. This is due to the fact that U.S. Pat. No.7,577,464 provides anti-jam GPS protection by varying controllable loadslocated within the antenna aperture, thus changing the properties of theantenna modes. Since monopulse direction-finding requires stable or atleast known antenna modes/patterns, it is not possible to provideprotection against sources of interference while simultaneouslyobtaining direction-finding measurements with the design provided byU.S. Pat. No. 7,577,464.

In summary, some major drawbacks of known radio-navigation systems thatprovide platform position, velocity, attitude and time (PVAT) estimatesare:

-   -   Simultaneous interference rejection capability and 3-D attitude        measurements (roll, pitch and yaw) are provided by very large        (D>>0.7λ) multi-aperture antenna arrays;    -   Phase interferometry-based 3-D GPS/A systems require large        baselines (D>0.7λ) and the required total antenna aperture is        unacceptably large for many applications;    -   Single-aperture satellite-based navigation systems are unable to        provide PVAT estimates while simultaneously providing protection        against sources of interference;    -   Single-aperture multi-mode direction-finding antennas have a        limited operational field-of-view for accurate angle-of-arrival        measurements;    -   Single-aperture multi-mode direction-finding antennas require an        analog mode-forming network, which increases hardware costs and        the size and weight of the system;    -   Radio-based navigation receivers capable of 3-D        attitude-determination rely on phase-interferometry methods or        sequential sampling of direction-finding antenna modes; and    -   Single-aperture and multi-aperture GPS/A systems can only        provide roll angle measurements for small (D<0.7λ) spinning        platforms, and are incapable of providing roll, pitch or yaw        angle measurements for non-spinning platforms.

INTRODUCTORY DEFINITIONS

Radio-based navigation systems require either single-element ormulti-element antennas for receiving RF signals. A multi-element antennaincludes at least two antenna elements. An antenna element comprises asingle driven element and associated parasitic elements, if any, andparasitic loads, if any. A driven element is a radiating element thathas at least one RF feed. A radiating element is defined as the smallestpossible subcomponent of an antenna that can receive and/or radiateelectromagnetic (EM) energy on its own. An element that radiates withoutan RF feed is referred to as a parasitic element [IEEE Std. 145, 1993].A non-radiating subcomponent without an RF feed is called a parasiticload. Parasitic loads can be either active or passive and may compriseresistive and/or reactive components, and may be controlled.

A single-element antenna is by definition a single-aperture system.However, a multi-element antenna can be classified as either asingle-aperture or a multi-aperture system. A traditional array antenna[IEEE Std. 145, 1993] with n identical antenna elements in a regulararrangement achieved by simple translations is an example of amulti-aperture system. However, although an n-arm spiral can beconsidered to be an array of n identical antenna elements (arms) in aregular arrangement achieved through simple rotations, it is also asingle-aperture system with an array of n cylindrically (rotationally)symmetric antenna elements (arms).

Whether an antenna is a single-aperture or a multi-aperture system isdetermined herein by its physical structure, and specifically aprojection of the antenna elements onto a plane surface on or near theantenna “perpendicular to the direction of maximum radiation, throughwhich the major part of the radiation passes” [IEEE Std. 145, 1993]. Thearea defined by the projection for antenna element X_(j) is defined asits radiating aperture A_(j)(X_(j)). The radiating aperture willhereinafter be referred to simply as aperture. The aperture of the jthantenna element can be precisely specified by the projection of itsconvex hull H_(j)(X_(j)) onto said plane surface:A_(j)(X_(j))=proj(H_(j)(X_(j))). In simple terms, the convex hull is theregion defined by a hypothetical rubber band (or rubber surface) thatphysically stretches over and encloses the entire antenna element.Mathematically, it is:

$\begin{matrix}{{{H_{j}\left( X_{j} \right)} = \left\{ {\left. {\sum\limits_{i = 1}^{k}{\alpha_{i}x_{i}}} \middle| {x_{i} \in X_{j}} \right.,{\alpha_{i} \in },{\alpha_{i} \geq 0},{{\sum\limits_{i = 1}^{k}\alpha_{i}} = 1},{k = 1},2,\ldots}\mspace{14mu} \right\}},} & (1)\end{matrix}$

where X_(j) is the set of all points contained by the jth antennaelement. An n-element antenna is defined to be a multi-aperture systemif the area of the intersection of the apertures of all antenna elementsis less than the area of the smallest aperture:

∥A ₁(X ₁)∩ . . . ∩A _(n)(X _(n))∥<min{∥A ₁(X ₁)∥, . . . ,∥A _(n)(X_(n))∥}.  (2)

Otherwise, it is a single-aperture system.

BRIEF SUMMARY

The present exemplary embodiments provide a small, single-aperture,multi-mode, direction-finding, controlled receive-pattern antenna (CRPA)and a direction-finding (DF) radio-navigation receiver system forsimultaneous interference rejection and position, velocity, time andattitude-determination.

A novel DF antenna design improves the gain and phase symmetry ofrotationally symmetric, single-aperture, multi-mode direction-findingantennas, which leads to accurate angle-of-arrival (AOA) measurementsover the entire hemisphere and, thereby, attitude-determinationperformance.

The DF radio-navigation receiver provides an adaptive capability formitigating the adverse impacts of interference on radio-based navigationsystems while simultaneously providing platform position, velocity, 3-Dattitude and time (PVAT) estimates that are drift-free and insensitiveto temperature variations. In contrast to existing multi-apertureGPS-based attitude (GPS/A) sensors, the present exemplary embodimentrelies on monopulse DF (simultaneous lobing) techniques instead ofinterferometry for determining attitude. Unlike phase interferometry,monopulse direction finding relies on the properties of the antennapatterns to determine the signal AOA. The accuracy of aninterferometer-based system depends on the length of the baseline, whilethe accuracy of monopulse DF depends on the known antenna patterns. Like(multi-aperture) array antennas, the DF receiver system can enhance thejammer-to-signal (J/S) tolerance of the receiver through beam formingand null steering while simultaneously measuring the angle-of-arrival ofan emitter. Alternatively, if no jamming is present, the signal-to-noiseratio (SNR) of each GPS signal can be improved (enhanced) byappropriately weighting and summing each antenna input signal. If theemitter position is unknown, the AOA measurement can be used to estimatethe position of the signal source. As described in U.S. Pat. No.7,577,464, a closed-loop AOA estimation process that refines the AOAestimates based on the platform dynamics can also be used to geolocatethe unknown position of an emitter and improve AOA measurement accuracy.If the emitter position is known (as it is with GPS), the AOAmeasurement can be used to determine the platform attitude.

The novel direction-finding radio-navigation receiver accepts inputsfrom any DF antenna with at least two feed ports that is capable ofsupporting at least two rotationally symmetric DF antenna modes. Somenovel advantages of the exemplary embodiments are:

-   -   A compact single-aperture multi-mode direction-finding and        anti-jam antenna with improved angle-of-arrival measurement        accuracy over an entire hemisphere;    -   A compact single-aperture multi-mode direction-finding and        anti-jam antenna with a 50% larger operational region compared        to existing single-aperture DF antennas;    -   No requirement for an analog mode-forming network for multi-mode        DF antennas, thus eliminating bulky hybrid couplers and phase        shifters;    -   Permits direct manipulation of radio-based navigation signals        from each antenna feed, or equivalently, of each antenna mode of        a multi-mode DF antenna for interference rejection and adaptive        beam forming;    -   A radio-based attitude determining receiver architecture with a        reduced number of code- and carrier-tracking loops for measuring        position, velocity, attitude, and time using a multi-mode        direction-finding antenna;    -   A radio-based DF navigation receiver capable of providing 3-D        attitude measurements for small spinning and non-spinning        platforms using a DF antenna having at least two rotationally        symmetric DF modes;    -   Simultaneous adaptive beam forming and radio-based 3-D attitude        measurement capability with a small single-aperture or        multi-aperture DF antenna;    -   Significant improvement in system robustness and attitude        accuracy when the radio-based navigation system is coupled with        low-cost gyroscopes, magnetometers, and alternative sensors; and    -   Significant improvement in system robustness and navigation        accuracy when the radio-based navigation system is coupled with        the platform guidance and control.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram showing components of the radio-baseddirection-finding navigation system capable of simultaneous interferencerejection while providing position, velocity attitude and time (PVAT)estimation using a multi-mode direction-finding antenna.

FIG. 2 is a block diagram of the preferred embodiment for a front-endreceiver processor that supports simultaneous interference rejection andPVAT estimation with a single-aperture two-arm spiral direction-findingantenna.

FIG. 3 illustrates the major components of spiral antennas.

FIG. 4 specifies the phasing for Modes 0, 1, 2, and 3 of a four-armspiral antenna.

FIG. 5 specifies the relative phasing required between successive armsof an n-arm spiral antenna in order to support Mode m=0,1, . . . , n−1.

FIG. 6 illustrates the gain patterns for Mode 0 and Mode 1 of a two-armspiral antenna.

FIG. 7 defines the antenna geometry, the coordinate system and thecomposite angle error.

FIG. 8 provides an example of the mean relative magnitude between Mode 0and Mode 1 of a two-arm spiral antenna as a function ofelevation/boresight angle.

FIG. 9 provides an example of the mean relative phase between Mode 0 andMode 1 of a two-arm spiral antenna as a function of azimuth angle.

FIG. 10 illustrates a two-arm spiral antenna design with a conductivevertical extension of the ground plane (conductive cavity wall) aboutthe antenna perimeter.

FIG. 11 illustrates a two-arm spiral antenna design with a conductivecavity wall and conductive posts about the antenna perimeter.

FIG. 12 shows the Mode 1 current distribution for a two-arm spiral withconductive posts and a conductive wall.

FIG. 13 shows the Mode 0 current distribution for a two-arm spiral withconductive posts and a conductive wall.

FIG. 14 shows the composite angle error of a two-arm spiral antennadesign with a conductive cavity wall and conductive posts.

FIG. 15 compares the composite angle errors of a two-arm spiral designwith and without conductive cavity walls and conductive posts.

FIGS. 16-17 illustrate the relative magnitude between Mode 0 and Mode 1for two-arm spiral designs with and without conductive cavity walls andconductive posts.

FIGS. 18-19 depict the asymmetry envelope about the mean relativemagnitude of two-arm spiral antenna designs with and without conductivecavity walls and conductive posts.

FIGS. 20-21 show the relative phase between Mode 0 and Mode 1 fortwo-arm spiral designs with and without conductive cavity walls andconductive posts.

FIGS. 22-23 depict the asymmetry envelope about the mean relative phaseof two-arm spiral antenna designs with and without conductive cavitywalls and conductive posts.

FIG. 24 provides examples of the null forming capabilities of a two-armspiral antenna for jammers at different elevation angles.

FIG. 25 shows the basic single input correlation architecture used inmost GPS receivers.

FIG. 26 provides a preferred embodiment of a correlation architecturefor GPS-based attitude estimation and interference rejection using aminimal number of mixers, correlators, and carrier- and code-loopnumerically controlled oscillators (NCOs).

FIG. 27 provides an alternative correlation architecture for GPS-basedattitude estimation and interference rejection with a reducedcomputational burden using a minimal number of mixers, correlators, andcarrier- and code-loop NCOs.

FIG. 28 provides an illustration of Wahba's problem for determining theattitude of a platform based on measured angle-of-arrival vectors(a_(j)) and known line-of-sight vectors (r_(j)).

FIG. 29 illustrates the 3-D attitude (roll, pitch and yaw) accuracy of atwo-arm spiral antenna with a conductive cavity wall and conductiveposts as a function of the number of satellites in track.

FIG. 30 provides an alternative design capable of providing simultaneousinterference rejection and PVAT estimates with a two-arm spiral antennausing an analog mode-forming and/or pattern/beam-forming network.

FIG. 31 shows the composite angle power spectral density (PSD) of aGPS-based attitude sensor when integrated with low-cost MEMS gyroscopes.

FIG. 32 illustrates a completely integrated guidance, navigation andcontrol architecture with simultaneous interference rejection and PVATestimation capabilities.

FIG. 33 illustrates the geometry of a spin-stabilized platform with thesingle-aperture DF antenna boresight aligned with the roll axis.

FIG. 34 is illustrates an alternative architecture for spin-stabilizedplatforms where the digital mode-forming network and a roll demodulationmodule precede the interference suppression module.

FIG. 35 explicitly illustrates the roll demodulation feedback loopimplied by FIG. 34.

FIG. 36 illustrates the roll demodulation geometry of a spin-stabilizedplatform with the boresight of a multi-aperture DF antenna aligned withthe platform roll axis.

DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS

Referring now to the drawings, which are intended to illustratepresently preferred exemplary embodiments of the invention only and arenot for the purpose of limiting same, a basic block diagram of aradio-based direction-finding navigation system using a multi-modedirection-finding antenna capable of interference rejection whilesimultaneously providing position, velocity, attitude and timemeasurements is shown in FIG. 1. The main components of the presentexemplary embodiment are (a) a multi-mode direction-finding antenna 1with at least two feed ports 2 that is capable of supporting at leasttwo spherical antenna modes 11; (b) an RF-to-digital front-end 3 thatreceives n analog signals from the antenna feed ports 2 and outputs mintermediate-frequency (IF) or baseband digital feed signals 4; and (c)a digital radio receiver and navigation processor 5 that accepts theIF/baseband digital feed signals 4 and outputs position, velocity,attitude and time estimates 6 while simultaneously providing protectionagainst sources of narrowband and wideband interference. The digitalradio receiver and navigation processor is also referred to as a digitalelectronics receiver module. The system can optionally accept inputsfrom additional sensors 7 and from the platform 9. Optional connectionsare shown as dashed arrows.

The present exemplary embodiment improves the angle-of-arrivalperformance of the multi-mode direction-finding antenna 1 through theuse of a conductive vertical extension of the ground plane about theperimeter of a single-aperture direction-finding antenna. The verticalextension of the ground plane effectively creates a conductive cavitywall, or a “can” about the antenna that improves the pattern symmetry ofthe spherical antenna modes. Similar performance improvements areobtained by using multiple conductive posts/pins about the antennaperimeter that are connected to the ground plane, but not to the antennaelement. A design making simultaneous use of the conducting cavity walland the conducting posts for improved symmetry is preferred. Thespecific height of the conductive cavity and/or posts depends on thedesired antenna performance characteristics such as symmetry, bandwidthand gain.

The signals from the antenna feed ports 2 (A1, . . . , An) aresynchronously down-converted by the RF-to-digital front-end 3 to anintermediate or baseband frequency and sampled. A digital down-converter(DDC) then reduces the signals to baseband. Identical signal pathlengths, a common clock and common phased-lock loops for all feedsignals will reduce relative magnitude and relative phase errors andimprove attitude measurements. The RF-to-digital front-end 3 outputs area set of digital feed signals at baseband 4. The baseband signals 4 (B1,. . . , Bm) with n≧m are provided to the radio receiver and navigationprocessor 5. The radio receiver and navigation processor 5 measures anangle-of-arrival for radio-based navigation signals while simultaneouslyproviding anti-jam protection against both narrowband and widebandinterferers and estimating platform position, velocity, attitude andtime 6 (PVAT).

An architecture for the digital electronics receiver module (radioreceiver and navigation processor) 5 capable of providing protectionagainst sources of interference while simultaneously measuring attitudeis shown in FIG. 2. In this preferred embodiment the multi-modedirection-finding antenna 1 of FIG. 1 is a single-aperture two-armspiral design 1 d. However, from the perspective of thedirection-finding receiver, the only requirement on the DF antenna isthat it must have at least two feed ports and support at least tworotationally-symmetric direction-finding modes. In fact, the antenna canbe a single- or multi-aperture design comprising one or more drivenelements. An example of a single-aperture single-element DF antenna isthe circular patch [Huang 1984].

Synchronously down-converted digital feed signals at baseband 4 a and 4b from each antenna arm are provided to a digital mode-forming network(DMFN) 23 and an interference suppression module (ISM) 21 embeddedwithin a front-end receiver processor 24. The purpose of the front-endreceiver processor 24 is to provide protection against broadband andnarrowband interference and to acquire and track select RFsignals-of-interest. For GPS-based satellite navigation systems each GPSsatellite signal is an RF signal-of-interest. In addition, the front-endreceiver processor 24 outputs basic in-phase (I) and quadrature-phase(Q) measurements 35 derived from the digital feed (baseband) signals 4 aand 4 b to a back-end processor 25.

Embedded within the front-end receiver processor 24 the digitalmode-forming network 23 outputs a digital Mode 1 signal 29 (M1) and adigital Mode 2 signal 30 (M2) corresponding to the spherical antennamodes 11 a of the two-arm spiral DF antenna 1 d. For two-arm spirals,the terms “Mode 0” and “Mode 2” are equivalent and can be used tointerchangeably. The interference suppression module 21 outputs theprimary navigation signal 31 (S). While the primary navigation signal 31(S) is used to estimate platform position, velocity and time, therelative magnitude and phase of the Mode 1 and Mode 2 signals 29 (M1)and 30 (M2) are used to determine the angle-of-arrival of thesignals-of-interest and the antenna attitude [Wahba 1965, Farrell 1966,Cohen 1996]. The Mode 1 signal 29 (M1) and the Mode 2 signal 30 (M2), aswell as the primary navigation signal 31 (S), are input into a frequencyexcision module 22 that outputs signals 29 a (M1), 30 a (M2), and 31 a(S). The interference suppression module 21 provides protection againstbroadband interferers, while the frequency excision module 22 providesprotection against narrowband interferers. Numerous and well knownmethods of narrowband and broadband interference suppression techniquesexist [Compton 1988, Ghose 1996] and will not be discussed here indetail. Broadband interference rejection requires forming a spatial nullin the direction of the jamming source that is broadband in nature. Acomplex weight is applied to each feed signal, or equivalently, eachmode signal, and the weighted signals are summed to achieve a desiredobjective, such as maximizing signal-to-interference-plus-noise (SINR),SNR, or simply to minimize noise power. A performance feedback signal 32(W₁), such as bit error rate (BER), SNR or SINR, is useful (but notnecessary) to make certain that the desired objective is obtainedwithout eliminating the signal of interest. The use of a multi-modesingle-aperture DF antenna as an array for broadband interferencesuppression is novel and highly useful and has not been done prior tothe present invention. Narrowband interference rejection requiresplacing spectral nulls (notch filters) at the frequencies withinterference. Simple fast Fourier transforms (FFT) can be used toachieve this goal by zeroing out frequency bins with too muchinterference power. The second performance feedback signal 33 (W₂) isalso optional for narrowband interference suppression. The twoperformance feedback signals 32 (W₁) and 33 (W₂) are desirable formaintaining the quality of performance of the system.

Monopulse direction finding and angle-of-arrival determination ispossible if the complex ratio of the Mode 1 and Mode 2 signals 29 (M1)and 30 (M2) remains unchanged in magnitude and phase after processing.It is possible to preserve the complex ratio of signals 29 (M1) and 30(M2) with narrowband frequency excision, but not with broadbandinterference suppression or null/beam steering. This is becausebroadband interference suppression requires spatial nulling thatmanipulates the spherical modes of the antenna, thereby losingangle-of-arrival information. Therefore, while the Mode 1 and Mode 2signals 29 a (M1) and 30 a (M2) do not directly benefit from protectionagainst broadband interference, they are provided direct protectionagainst narrowband interference. However, the Mode 1 and Mode 2 signals29 a (M1) and 30 a (M2) can benefit indirectly from the broadbandprotection provided by the interference suppression module 21 if theprimary navigation signal 31 a (S) is used to assist in acquiring andtracking the Mode 1 and Mode 2 signals.

The process of acquiring and tracking of signals is accomplished withina correlation module 26 embedded in the front-end receiver processor 24.The purpose of the correlation module 26 is to acquire and tracksignals-of-interest and to output the basic measurements 35 to theback-end processor 25 for PVAT estimation and navigation. In a GPS-basedsystem the basic measurements 35 are the in-phase (I) andquadrature-phase (Q) signals obtained by removing the carrier and code(and data) from each satellite signal (signals-of-interest). Thisprocess is sometimes referred to as carrier-wipeoff and code-wipeoff(and data-wipeoff) and is made possible with knowledge of the receivedwaveform. In order to obtain GPS signal angle-of-arrival measurements,the process of carrier-wipeoff and code-wipeoff must also be applied tothe Mode 1 and Mode 2 signals 29 a (M1) and 30 a (M2) in addition to theprimary navigation signal 31 a (S) for each satellite being tracked. Thepresent exemplary embodiment introduces correlation architecture thatmakes it is possible to acquire and track s satellites and obtainattitude measurements with only s acquisition and carrier- andcode-tracking loops and a minimal number of mixers and correlators.

The primary purpose of the back-end processor 25 is to properly processthe basic measurements 35 in order to estimate and output the platformposition, velocity, attitude and time 6 (PVAT). The secondary purpose ofthe back-end processor 25 is to provide feedback to the front-endreceiver processor for improved interference suppression, frequencyexcision and coherent correlation. A broadband performance metric signal32 (W₁) and a narrowband performance metric signal 33 (W₂) can be fedback to the interference suppression module 21 and the frequencyexcision module 22 to ensure that the signal-to-interference-plus-noiseratio is being maximized. A vector signal 34 (δf) is used to assist thecorrelation process and specifically the carrier- and code-trackingloops with Doppler corrections and/or pseudo-range rate estimates foreach satellite. The architecture shown in FIG. 2 is compatible withtraditional GPS receiver designs, as well as loosely-coupled,tightly-coupled and ultra-tightly coupled (UTC) GPS/INS systems. Thespecific receiver, interference rejection and navigation algorithmsimplemented within the front-end receiver processor 24 and the back-endprocessor 25 are application dependent. The present exemplary embodimentalso permits the detection of multipath when the actual angle-of-arrivalof an inbound signal is significantly different from the expectedangle-of-arrival.

In summary, an exemplary embodiment provides a compact radio-baseddirection-finding navigation system capable of offering simultaneousprotection against sources of interference while providing position,velocity, attitude and time measurements with a large operationalfield-of-view antenna.

Another aspect of the exemplary embodiment is to provide a smallsingle-aperture multi-mode direction finding antenna requiring as few astwo feeds and supporting at least two spherical modes that are capableof being used for simultaneous interference rejection and accurateangle-of-arrival measurements over an entire hemisphere.

The exemplary embodiment also provides protection against sources ofinterference, while simultaneously obtaining accurate attitudemeasurements over the entire hemisphere using a small single-aperturemulti-mode direction-finding antenna with as few as two feeds thatsupports at least two spherical antenna modes.

Further objects and advantages of the present invention will becomeapparent from a consideration of the accompanying drawings and ensuingspecification. Although the presently preferred exemplary embodimentrelates to GPS-based position and attitude measurements, it isunderstood that the novel advantages of the exemplary embodiments mayalso apply to any radio-based navigation system or alternativesignals-of-opportunity such as television and radio signals where thepositions of the satellites or emitters and signal waveforms are known apriori.

Single-Aperture Multi-Mode Direction-Finding Antenna

An example of the multi-mode direction-finding antenna 1 is a four-armspiral antenna 1 a shown in FIG. 3 and its planar, conformal, conical orslotted variations such as a square spiral, Archimedean spiral,equiangular spiral, and the logarithmic spiral. Antennas may becavity-backed or printed microstrip designs with or without a groundplane, and possibly slotted. Other examples of DF antennas includecircular patches [Huang 1984], sinuous antennas, multi-mode hornantennas, and circular arrays of log periodic antennas fed by a Butlermatrix. The specific choice of the single-aperture multi-modedirection-finding antenna depends primarily on the application and thelimitations of the antenna platform.

FIG. 3 illustrates the structure of a four-arm Archimedean microstripspiral antenna 1 a which comprises some of the basic components ofsingle-aperture DF antennas including an antenna substrate 15 supportingfour conductive arms 12(a-d) and four feeds 13(a-d), as well as adielectric space 14 between a ground plane 16 and the antenna substrate15. The counterclockwise direction of the spiral arms is selected toreceive primarily right-hand circularly-polarized (RHCP) signals.Left-hand circularly-polarized (LHCP) antennas can be constructed byreversing the direction of the spirals, or by placing the feeds at theouter perimeter of the antenna elements (arms). Simultaneous LHCP andRHCP reception is possible by placing feeds both at the innermost andoutermost radii of the antenna arms.

The physical structure of the antenna systems described herein can varyto meet the size and cost constraints of the platform upon which theantenna is placed. The minimum diameter (d_(min)) required for n-armspiral antenna for direction-finding is determined by the maximum modenumber m_(max) used, or

$\begin{matrix}{{d_{\min} = {{\frac{m_{\max}}{\pi \sqrt{ɛ_{r}}}\lambda} = {\frac{m_{\max}}{\pi \sqrt{ɛ_{r}}}\frac{c}{f}}}},} & (3)\end{matrix}$

where m_(max)=1,2, . . . , n−1, λ is the wavelength and f is thefrequency of the signal of interest. The speed of light is denoted by cand ∈_(r) is the dielectric constant relative to free space. Hence, atwo-arm spiral supporting Mode 0 and Mode 1 (m_(max)=1) and operating inthe L1 band (1575.42 MHz±12 MHz) using a substrate with Å_(r)≅1 requiresa diameter of at least 6.1 cm (2.4 in). For operation in both the L1 andL2 (1227.6 MHz±12 MHz) frequency bands, a two-arm spiral antenna with adiameter of at least a 7.9 cm (3.1 in) is necessary with Å_(r)=1.Relative to wavelength,

${\frac{d_{\min}}{\lambda} \geq \frac{m_{\max}}{\pi \sqrt{ɛ_{r}}} \cong {0.32\mspace{14mu} {for}\mspace{14mu} m_{\max}}} = {{1\mspace{14mu} {and}\mspace{14mu} ɛ_{r}} = 1.}$

Hence, the largest dimension of a two-arm spiral DF antenna need not beany larger than about one-third of a wavelength. In contrast, a four-armspiral using Mode 1 and Mode 2 (m_(max)=2) for direction finding willrequire at least two-thirds of a wavelength with ∈_(r)=1, or

$\frac{d_{\min}}{\lambda} \geq {0.64.}$

While the use of higher dielectrics allows for a smaller antennadiameter for the purposes of impedance matching, the interferencerejection and direction-finding performance of the system will besomewhat diminished.

The material used for a printed antenna element may generally be copper,but other conductive materials can also be used. The antenna substrate15 may generally be of dielectric material such as Duroid® and isnormally placed above a conductive panel that forms the ground plane 16.The dielectric space 14 between the antenna substrate 15 upon which theantenna arms 12(a-d) are printed and the ground plane 16, if any, may befilled with air or some other material with a higher relative dielectricconstant. Given footprint constraints, the microstrip geometry, and theproperties of this dielectric material, the height of the element abovethe ground plane must be chosen to best tune the antenna over thefrequencies of interest.

The antenna is electrically connected to the feeds 13(a-d), at suitablychosen points on the antenna arms 12(a-d). In general, the feeds areelectrically connected to ports that are attached to the RF-to-digitalfront-end electronics 3 prior to the digital radio receiver andnavigation processor 5. In traditional designs the RF front-endelectronics includes an analog mode-forming network like a Butler matrix[Mosko 1984]. Although the present exemplary embodiment eliminates theanalog mode-forming network in favor of a digital mode-forming network,it is clear that it does not need to do so. Furthermore, in the contextof the above description, it should be readily understood that while theantenna as described here is in a planar configuration, this antennacould be designed conformally to a convex or concave shape. In thissituation, reference to a “plane” or a surface that is “flat” would begeneralized to imply simply a continuity of surface, whether curved orflat.

Multi-mode DF antennas such as the four-arm spiral 1 a of FIG. 3 provideangle-of-arrival information by measuring the relative gain and/or phaseof two or more antenna modes. For example, as shown in FIG. 4, Mode 0for a four-arm spiral antenna design requires relative phasing of 0°between adjacent arms (i.e., sequentially 0°, 0°, 0°, 0°) while Mode 1requires 90° (i.e., sequentially 0°, 90°, 180°, 270°) and Mode 2requires 180° (i.e., sequentially 0°, 180°, 360°, 540°). Generallyspeaking, and as specified in FIG. 5, Mode m (=0,1, . . . , n−1) for ann-arm spiral antenna is achieved by applying a relative phasing betweenadjacent arms of 360 m/n degrees prior to summation. Mode 0 in a n-armspiral design is sometimes referred to as Mode n. Herein the terminology“Mode 0” or “Mode n” is used interchangeably and there is no confusionas long as n is specified. Hence, for our purposes the terms “Mode 0”and “Mode 2” are deemed to be equivalent for two-arm spiral designs.However, Mode 2 for a four-arm spiral antenna should not be confusedwith Mode 0 of a two-arm spiral antenna as they are not equivalent.

FIG. 6 shows the right-hand-circularly-polarized (RHCP) magnitudes 11 aof Modes 0 and 1 for a two-arm spiral antenna. Elevation angle (θ) isrelated to the relative magnitudes of two or more modes whereas azimuthangle (φ) is related to the relative phases. Elevation and azimuthangles are defined in polar coordinates by the geometry shown in FIG. 7.The elevation angle (θ≧φ) is sometimes referred to as the boresightangle or zenith angle and is defined as the angle difference between theline-of-sight (LOS) vector and the antenna boresight (z-axis). Theazimuth is defined in a right-handed sense as the angle (−π<φ≦π) betweenthe x-axis and the projection of the LOS vector on the xy-plane, and isundefined at the antenna boresight θ=0. The angle-of-arrival accuracy ofdirection-finding antennas can be efficiently described by the compositeangle error. The composite angle error is defined as:

σ_(c) ²=σ_(θ) ²+sin²(θ)σ_(φ) ²,  (4)

where σ_(θ) is the one-sigma elevation angle error and σ_(φ) is theone-sigma azimuth angle error. The composite angle error defines anerror cone about the LOS vector and discounts azimuth errors near theboresight where they are undefined. The elevation and azimuth angleerrors are usually functions of elevation and azimuth:

σ_(c) ²(θ,φ)=σ_(φ) ²+sin²(θ)σ_(φ) ²(θ,φ),  (5)

FIG. 8 shows the relationship between elevation angle and the relativemagnitude of Mode 0 with respect to Mode 1 of a two-arm spiral antenna.It is clear that a relative gain measurement provides information aboutthe elevation angle. FIG. 9 illustrates the relationship between azimuthangle and relative phase of Mode 0 with respect to Mode 1 for the sameantenna. Similarly, it is clear that a relative phase measurementprovides information about the azimuth angle. Hence, one can determinethe angle-of-arrival of a signal by measuring the relative magnitude andthe relative phase between two or more modes and comparing thosemeasurements with known properties of the DF antenna, possibly throughthe use of table lookups and optimization [U.S. Pat. No. 7,577,464]. Analternative method of determining the angle-of-arrival is through theuse of a pattern- or beam-forming network and measuring only therelative magnitude between two or more patterns [Mosko 1996].

The 3-D attitude (roll, pitch, and yaw/heading) of the antenna can bedetermined from the angle-of-arrival of two or more signals if thereceiving antenna position and the origin of the received signals areknown [Wahba 1965, Farrell 1966, Cohen 1996]. U.S. Pat. No. 5,461,387describes an instrument for determining attitude using Modes 1 and 2 ofa spiral antenna with three or more arms (feeds). The present exemplaryembodiment differs significantly from the teachings of U.S. Pat. No.5,461,387 in several ways. For example, in contrast to U.S. Pat. No.5,461,387, the present exemplary embodiment requires a DF antennacapable of supporting at least two modes, but is not limited to the useof only Mode 1 and Mode 2. Specifically, U.S. Pat. No. 5,461,387excludes the use of two-arm single-aperture DF antennas capable ofsupporting Mode 0 and Mode 1, such as the spiral shown in FIG. 10. Asmentioned earlier, this is because prior teachings [U.S. Pat. No.4,630,064 and Corzine 1990] indicated that two-arm spiral antennas wereinappropriate for direction-finding applications. This is importantbecause as indicated by Equation (3) the circumference of a three- orfour-arm spiral antenna capable of supporting Mode 1 and Mode 2 must beat least two wavelengths (2λ) whereas a two-arm spiral antennasupporting Mode 0 and Mode 1 only requires a circumference of onewavelength (λ). Hence, the generalization to two-arm spirals reduces thesize of the minimum required antenna aperture by 75% and the minimumantenna diameter by 50%, thereby greatly increasing the number ofrelevant platforms and applications for this system. For example, theminimum required diameter of a spiral antenna at 1575 MHz with air as asubstrate is reduced from 12.1 cm to less than 6.1 cm. Thisminiaturization allows the system to be placed on much smaller platformssuch as micro air vehicles (MAVs).

Furthermore, the present exemplary embodiment also permits the use ofmore than two modes for improved angle-of-arrival and attitude accuracy,which is not taught by U.S. Pat. No. 5,461,387. For example,simultaneous measurements from Mode 0, Mode 1, Mode 2 and Mode 3 of afour-arm spiral antenna can be used for improved angle-of-arrivalestimation [Penno 2001]. In addition, the present exemplary embodimenteliminates the need for the analog feed/mode-forming network required byU.S. Pat. No. 5,461,387. Instead, the modes are digitally formed thuseliminating significant hardware and reducing the size and cost of thesystem. The elimination of the analog mode-forming network is nottrivial and requires special care in the antenna design so that eachfeed port is sufficiently isolated from the rest of the ports. Finally,the present exemplary embodiment introduces a simultaneous interferencerejection capability with a single-aperture multi-mode direction-findingantenna that is not anticipated by U.S. Pat. No. 5,461,387, or any otherprior art.

The design of the multi-mode direction-finding antenna 1 has beenimproved for better angle-of-arrival accuracy and increasedhemispherical coverage. As illustrated with a two-arm spiral antenna 1 bdesign in FIG. 10, the present exemplary embodiment introduces aconductive vertical extension 17 of the ground plane 16 at the antennaperimeter. The conductive vertical extension 17 of the ground plane 16at the antenna perimeter creates a conducting cavity wall or “can”around the antenna. The height of the conducting cavity wall above theground plane 16 depends on the desired bandwidth, frequency, and patternsymmetry properties of the antenna. The conductive vertical extension 17introduces boundary conditions about the antenna which forces thepatterns to remain significantly more symmetric about the antennaboresight. Hence, when the feed ports 2 a and 2 b are connected to adigital or analog mode-forming network, the resulting patterns havesignificantly less ripple magnitudes near the antenna horizon and atelevation/boresight angles greater than 50°.

As shown in FIG. 11 the conductive vertical extension 17 can be replacedor augmented with conductive posts (pins) 19(a-d), that are electricallyconnected to the ground plane 16 or the conductive vertical extension 17at the antenna perimeter. However, the conductive posts (pins) are notelectrically connected to the spiral-arms. Often, the height of theconductive vertical extension 17 need not reach the antenna substrate15. Instead, a dielectric gap 20 between the antenna substrate and theconductive vertical extension 17 may be desired with conductive posts19(a-d) of height equal to the dielectric gap 20 and electricallyconnected to the conductive vertical extension 17. The height of theconductive cavity wall 17 and the conductive posts 19(a-d), as well asthe number of posts depend on the desired bandwidth, frequency, andpattern symmetry properties of the antenna. For best results, thelocation of the posts along the antenna perimeter should maintain therotational symmetry of the antenna. FIG. 11 shows a two-arm spiralantenna 1 c with four conductive posts 19(a-d) along the outer perimeterof the antenna. The location of the conductive posts 19(a-d), maintainsthe two-fold symmetry of the two-arm spiral antenna. In the limit, asthe number of posts increases and the gap between them decreases, thedesign approaches that of a conductive cavity wall equal to the heightof the conductive posts.

Counter to the teachings of U.S. Pat. No. 5,621,422, neither theconductive posts 19(a-d), nor the conductive vertical extension 17, areused to short the spiral arms 12 e and 12 f, or the antenna feeds 13 eand 13 f to the ground plane 16. In this manner the simultaneousexcitation of Mode 0 and Mode 1 is made possible. U.S. Pat. No.5,621,422 states that “[t]he shorting mechanisms, a total of four withone on each of the four arms, while enhancing mode-0, do not interferewith the other modes if the shorting mechanisms 62a, 62b [of FIGS. 6Aand 6B] are placed outside the radiation zones corresponding with thehigher-order spiral modes” [column 10, line 20]. However, U.S. Pat. No.5,621,422 omits the fact that if it is not possible to place theshorting mechanism “outside the radiation zone” of a higher-order spiralmode, such as Mode 1 for a two-arm spiral with a circumference of aboutone wavelength, then the shorting mechanisms actually cause asignificant degradation of the higher-order mode and, therefore, thedirection-finding performance of the antenna. FIG. 12 and FIG. 13 showthe Mode 1 and Mode 0 current distributions for a two-arm spiral antennawith four conductive posts and a vertical conducting wall. Needless tosay the two modes have significant overlap and the Mode 1 radiation zoneincludes the outer perimeter of the antenna. Hence, the shortingmechanism suggested by U.S. Pat. No. 5,621,422 is not feasible. Incontrast to the present exemplary embodiment, U.S. Pat. No. 5,621,422also requires the use of an analog mode-forming network prior to thedigitization of the received signals.

FIG. 14 shows the composite angle error of a two-arm spiral antenna fora signal-to-noise ratio (SNR) of 29 dB. The performance in FIG. 14corresponds to a 6.5 cm diameter two-arm spiral design optimized withthe conductive vertical extension 17 equal to 71% of the total antennaheight and the conductive posts 19(a-d), that extend up to the antennasubstrate 15. The conductive vertical extension and posts also providestructural support for the two-arm spiral antenna.

The accuracy of most DF systems degrades beyond a certain point based onthe incident geometry of the signal-of-interest. Single-aperture n-modedirection-finding antennas have gain patterns that exhibit n-foldsymmetry about their boresight. For constant elevation angle cuts theripples in their gain patterns repeat n times within a single revolutionabout the boresight axis, or an azimuthal rotation of 360°. Furthermore,the ripple amplitude increases near the antenna horizon (large elevationangles). Hence, the n-fold repetition in the gain patterns, and theincrease in ripple amplitude makes it difficult to obtain goodangle-of-arrival accuracy over the entire hemisphere. In fact, theuseful operating region of most single-aperture multi-mode DF antennasis less than 50% of the hemisphere, or elevation angles of less than60°. Moreover, many DF antennas are only useful for elevation angles ofless than 30°, or less than 13.4% of the hemisphere. The introduction ofthe conductive vertical extension 17 and/or conductive posts 19(a-d),reduces the asymmetry of the antenna patterns and significantly improvesthe angle-of-arrival/direction-finding performance of the system.

FIG. 15 compares the composite angle error performances of a two-armspiral design which were optimized with and without a conductive cavitywall or conductive posts. The two designs are otherwise the same sizeand height. As clearly indicated by FIG. 15 the performance of theantenna with a conductive vertical extension 17 and conductive posts19(a-d) is significantly better than the antenna missing these featuresabove an elevation angle of 50° and provides good AOA performance forthe entire hemisphere. Similar performance improvements were noted forsingle-aperture DF antennas with a greater number of arms/elements.Hence, the conductive vertical extension 17 of the ground plane 16 alongwith the conductive posts 19(a-d) at the antenna perimeter improves theangle-of-arrival accuracy of single aperture multi-modedirection-finding antennas and significantly extends their operationalregion to the entire hemisphere.

FIGS. 16-23 demonstrate the improvements in the pattern symmetry in bothmagnitude and phase due to the conductive vertical extension of theground plane, and the conductive posts around the antenna perimeter.FIGS. 16 and 17 show the magnitude of the complex relative gain M₀/M₁between Mode 0 and Mode 1 for a two-arm spiral with and without theconductive posts 19(a-d) or the conductive vertical extension 17 of theground plane 16. It is clearly apparent from FIG. 16 that there aresignificant ripples in the magnitude of the relative gain pattern nearthe antenna horizon, or elevation angles of greater than 60°. The rippleamplitude has been significantly reduced in FIG. 17 with theintroduction of the conductive posts 19(a-d) and conductive cavity wall17. This improvement is further quantified by FIGS. 18 and 19 that showthe asymmetry envelope about the mean relative magnitude at eachelevation angle for both antennas. In other words, FIGS. 18 and 19 showthe azimuthal variation in the magnitude of the relative gain at eachelevation angle. As seen in FIG. 18, the asymmetry envelope is about 30dB at the antenna horizon. That is to say, the variation of the relativemagnitude is about 30 dB at the antenna horizon. In contrast, thevariation at the horizon is less than 5 dB in FIG. 19. This is animprovement of over 25 dB. The variations shown in FIGS. 18 and 19 nearthe antenna boresight (θ=0) are primarily due to numerical inaccuraciescaused by the null in the Mode 0 antenna pattern and do notsignificantly contribute to the angle-of-arrival accuracy of theantennas.

Similar improvements in the relative phase are illustrated in FIGS.20-23. FIGS. 20 and 21 show the phase of the complex relative gain M₀/M₁between Mode 0 and Mode 1 for a two-arm spiral with and without theconductive posts 19(a-d) or the conductive vertical extension 17 of theground plane 16. Each figure shows the variation in relative phase forall elevation angles as a function of azimuth angle. Ideally we wouldlike this to be a very narrow straight line between −180° and 180°.Clearly, the family of curves shown by FIG. 21 is closer to the idealthan those shown by FIG. 20. The difference between these two figures isquantified by FIGS. 22 and 20 that show the phase variation due toelevation angle about the mean relative phase for each azimuth angle. Asillustrated by FIG. 22, the maximum peak-to-peak relative phasevariation for the traditional two-arm spiral design is about 100°. Incontrast, as shown by FIG. 23, the two-arm spiral design with theconductive cavity wall 17 and the conductive posts 19(a-d) has a maximumpeak-to-peak variation of 50°, or half the variation of the traditionaldesign.

Finally, as should be clear to those skilled in the art, thesymmetry-inducing design innovations introduced herein for the spiralantenna, namely, a conductive vertical wall and conductive pins, may beapplied to any rotationally symmetric single-aperture DF antenna,including any single-element (single-aperture) DF antenna such as themulti-mode circular patches described by [Huang 1984].

Digital Receiver and Processor Design

A novel direction-finding receiver and processor design is describedherein that provides protection against narrowband and broadbandinterference while simultaneously estimating position, velocity,attitude, and time with a compact multi-mode direction-finding antenna.Existing radio-based navigation receivers require either very largemulti-aperture antenna arrays with three or more antenna elements, orcannot provide protection against sources of broadband interferencewhile simultaneously obtaining direct attitude measurements with asingle-aperture antenna. Although the descriptions found herein referprimarily to satellite-based navigation systems, it will be clear to theperson skilled in the art that the present exemplary embodiment appliesto any signals-of-opportunity and radio signals originating from knownlocations and waveforms. It is also clear that the preferred embodimentis primarily a digital implementation. However, an analog implementationis an obvious extension.

As illustrated by the top-level system architecture shown in FIG. 1, thedigital radio receiver and navigation processor 5 accepts the digitalbaseband feed signals 4 output by the RF-to-digital front-endelectronics 3. The primary system output 6 is the estimate of theplatform position, velocity, attitude, and time. In the preferredembodiment, the primary function of the RF-to-digital front-endelectronics 3 is to down convert the antenna feed port signals 2 (A1, .. . , An) from the frequency of interest to an intermediate frequency(IF) or baseband, and to sample them with an analog-to-digital converter(ADC). A digital down-converter (DDC) may also be employed to bring IFsignals to baseband. The digital radio receiver and navigation processor5 must then properly processes the digital baseband feed signals 4 toestimate the platform PVAT while simultaneously providing protectionagainst broadband and narrowband interference.

Although the present exemplary embodiment applies to radio-basednavigation systems using an n-element, multi-mode DF antenna, thepreferred embodiment in FIG. 2 illustrates important features using atwo-arm (two-element) spiral antenna design. However, as it should beclear to those skilled in the art, the only requirement imposed on thedirection-finding antenna by the DF receiver is that it must have atleast two feeds and support at least two direction-finding modes. Hence,there are two digital baseband feed signals 4 a and 4 b to the digitalradio receiver and navigation processor 5. The digital radio receiverand navigation processor 5 comprises a front-end receiver processor 24and back-end navigation processor 25. The front-end receiver processor24 constructs the Mode 1 and Mode 2 signals 29 (M1) and 30 (M2) with thedigital mode-forming network 23 and provides protection againstbroadband and narrowband interference prior to coherently processing themeasured signals in the correlation module 26. The back-end processor 25fuses all available measurements with a navigation filter to estimatethe platform position, velocity, attitude, and time 6. Methods of fusingsensor measurements to compute position, velocity, attitude and time arewell known to those skilled in the art. One of the most commonapproaches is to employ a Kalman filter, or an extended Kalman filter(EKF), or other non-linear estimation techniques. The back-end processormay also provide some feedback to the front-end receiver processor 24 inthe form of a broadband performance metric signal 32 (W₁), a narrowbandperformance metric signal 33 (W₂), and a Doppler aiding signal 34 (δf).

Digital Mode-Forming Network

The mode-forming arithmetic for a two-arm spiral antenna is simple:

$\begin{matrix}{\begin{pmatrix}M_{1} \\M_{2}\end{pmatrix} = {{\begin{bmatrix}1 & {- 1} \\1 & 1\end{bmatrix}\begin{pmatrix}A_{1} \\A_{2}\end{pmatrix}} = {{T_{2}\begin{pmatrix}A_{1} \\A_{2}\end{pmatrix}}.}}} & (6)\end{matrix}$

FIG. 6 shows the resulting Mode 1 and Mode 2 gain patterns 11 a for thetwo-arm spiral antenna 1 d. In comparison, the four-arm spiral antennamode-forming arithmetic as specified by FIG. 4 is:

$\begin{matrix}{\begin{pmatrix}M_{1} \\M_{2} \\M_{3} \\M_{4}\end{pmatrix} = {{\begin{bmatrix}1 & ^{{- {j\pi}}/2} & ^{- {j\pi}} & ^{{- 3}{{j\pi}/2}} \\1 & ^{- {j\pi}} & 1 & ^{- {j\pi}} \\1 & ^{{j\pi}/2} & ^{j\pi} & ^{3{{j\pi}/2}} \\1 & 1 & 1 & 1\end{bmatrix}\begin{pmatrix}A_{1} \\A_{2} \\A_{3} \\A_{4}\end{pmatrix}} = {{T_{4}\begin{pmatrix}A_{1} \\A_{2} \\A_{3} \\A_{4}\end{pmatrix}}.}}} & (7)\end{matrix}$

Regardless, it should be clear that the antenna mode signals and thefeed signals are algebraically equivalent. For example, interferencesuppression can be done using either set of signals with equivalentperformance. In addition to reducing the cost and weight of the system,the digital mode-forming network 23 makes it easier to calibrate thesystem for gain and phase imbalances between the two RF channelsstarting with the feed ports 2 a (A1) and 2 b (A2). For example, acomplex frequency dependant function Δ(ω)∈C^(2×2) can be used to ensurethat the antenna Mode 1 and Mode 2 signals 29 (M1) and 30 (M2) aresymmetric about boresight and that the Mode 2 signal 30 (M2) has a nulldirectly on boresight:

$\begin{matrix}{\begin{pmatrix}M_{1} \\M_{2}\end{pmatrix} = {\left( {\begin{bmatrix}1 & {- 1} \\1 & 1\end{bmatrix} + {\Delta \; (\omega)}} \right){\begin{pmatrix}A_{1} \\A_{2}\end{pmatrix}.}}} & (8)\end{matrix}$

Calibration can be a completely automatic and closed-loop process. Thiswould be much more difficult and time consuming with an analogmode-forming network comprising combiners, 90° phase shifters and 180°quad couplers.

Interference Rejection

The architecture of FIG. 2 provides protection against broadband andnarrowband interference with the interference suppression module 21 andthe frequency excision module 22. The frequency excision module 22provides protection against narrowband interference signals while theinterference suppression module 21 provides broadband protection(nulling and beam forming). In a paradigm shift, the present exemplaryembodiment treats single-aperture multi-mode direction-finding antennassimilar to multi-element, multi-aperture antennas such as arrays [Penno2001, Penno 2002]. In other words, as long as the antenna supports atleast two DF modes (and two feeds), it makes no difference to thereceiver if the DF antenna is a single- or multiple-aperture system. Forexample, an n-arm spiral antenna is treated as an array of cylindricallysymmetrical n-elements. Hence, existing and well known algorithms[Compton 1988, Chose 1996] for broadband and narrowband interferencerejection can be applied with minor modifications [Penno 2002]. Thesealgorithms include space-time adaptive processing (STAP) andspace-frequency adaptive processing (SFAP) methods. The primarydifference in the implementation of those algorithms will be due to thefact that each arm of an n-arm spiral antenna will be 360/n degrees outof phase with its neighbor. In sharp contrast, conventional arraysystems assume that the pattern of each antenna element is identical.Nonetheless, similar to conventional antenna array systems, it is alsopossible to determine the angle-of-arrival of an interference sourcewith an array of cylindrically-symmetric elements while simultaneouslyplacing a null in its direction.

Although the embodiment shown in FIG. 2 indicates that the frequencyexcision module 22 follows the digital mode-forming network 23 and theinterference suppression module 21, it can be placed before or aftereither block. Mathematically speaking the specific order of said modulesis irrelevant. If desired, the frequency excision module 21 can operatedirectly on the digital baseband feed signals 4 a and 4 b prior to theinterference suppression module 21 and digital mode-forming network 23.An advantage of such an architecture is that it minimizes thecomputational burden by operating on only the two signals 4 a and 4 binstead of the three signals 29, 30 and 31.

The digital mode-forming network 23 can also precede the interferencesuppression module 21. In that case, the inputs to the interferencesuppression module 21 would actually be the Mode 1 and Mode 2 signals 29(M1) and 30 (M2). As indicated by Equations (6) and (7), themode-forming operation is reversible (T₂ and T₄ are invertible) and,hence, the digital feed signals 4 a and 4 b can be recovered by theinterference suppression module 21 with the application of a linear (andunnecessary) transformation.

The only restriction that is preferably observed in the design of thefront-end receiver processor 24 is that the Mode 1 and Mode 2 signals 29a (M1) and 30 a (M2) at the input to the correlation module 26 mustretain the same relative phase and gain as the Mode 1 and Mode 2 signals29 (M1) and 30 (M2) at the output of the digital mode-forming network23. Therefore, the same instantaneous gain and phase must be applied toboth the Mode 1 and Mode 2 signal channels. This restriction guaranteesthat the angle-of-arrival information for each signal-of-interest isretained and can be recovered for direction-finding and attitudeestimation. However, it also implies that it is not possible to offerthe Mode 1 and Mode 2 signals direct protection against broadbandinterference, although it is possible to provide them with directprotection against narrowband jammers. This is because the frequencyexcision module 22 will impart the same instantaneous gain and phase onboth the Mode 1 and Mode 2 signals 29 (M1) and 30 (M2). Later weintroduce a preferred embodiment for the correlation module 26 thatprovides the Mode 1 and Mode 2 signals indirect protection againstbroadband jammers.

FIG. 24 demonstrates the nulling performance of a two-arm spiral antennain response to a single broadband jammer for four different jammerorientations. The arrows indicate the direction of the jamming signaland the gain plot with the corresponding line style shows the typicalnull steering response of the system. As shown in FIG. 24 the null depthis in excess of 25 dB for all jammer orientations for the entire thehemisphere. A two-arm spiral antenna with two RHCP feeds can only null asingle broadband jammer that is linearly polarized or RHCP. However, atwo-arm spiral with two inner RHCP feeds and two outer LHCP feeds cansimultaneously null one purely RHCP and one purely LHCP jammer, or asingle linearly polarized jammer. In general, the number spatial nullsthat can be controlled by an n-arm spiral is n−1, the same as atraditional n-element array. The (best case) number of polarizationsensitive nulls that can be formed is 2n−1, provided the spiral has bothinner and outer polarization dependant feeds.

The frequency excision capability of the system against narrowband orcontinuous-wave jammers will depend primarily on the sampling resolutionand dynamic range of the analog-to-digital converters, as well as theprocessing power available. The software-radio approach to radio-basednavigation receivers now permits the use of fast Fourier transforms(FFTs) for acquisition, multipath mitigation, and narrowband frequencyexcision. While the depth of the narrowband (continuous-wave) CW nulldepends on the ADC resolution, the width of the null depends on thenumber of FFT bins and the signal bandwidth. For example, a 45 dB CWnull depth and a 0.4% null width are achievable with 10-bit accuracy anda 256-bin FFT. Narrower null widths are desirable in order to reduce thenegative effects of the notch filter on the radio signal. However,narrower null widths require more FFT bins which require more processingpower. Swept CW jammers require additional processing in order to trackthe swept signal. Hence, the CW nulling accuracy and the number ofsimultaneous CW nulls will be limited by the available processing power.Nonetheless, the embodiment shown in FIG. 2 is compatible with existingtime-based and frequency-based methods of frequency excision and isindependent of the specific implementation.

Given the basic measurements 35 of front-end receiver processor 24, theprimary function of the back-end processor 25 is to estimate theplatform PVAT 6. Another one of its functions is to provide feedback tothe front-end receiver processor 25 in the form of the broadbandperformance metric signal 32 (W₁) and the wideband performance metricsignal 33 (W₂). Broadband and wideband performance metrics may include abit error rate (BER), or some other quality-of-service (QoS) signalincluding, but not limited to, signal-to-noise ratio,signal-to-interference-plus-noise ratio, carrier-to-noise ratio (C/N₀)or jammer-to-noise ratio (J/N). The metrics may be a discrete state ormission time that is used to select between a set of fixed weights inthe interference suppression module 21 and/or the frequency excisionmodule 22. It is clear that the specific set of performance metricsignals chosen will depend on the application. We also note that theseparation of the front-end processor and the back-end processor blocksis artificial and is meant only as a tool for simplifying the generaldiscussion. Clearly all the processing can be done on a single chip oron multiple chips.

Coherent Correlation Module

The final component of the front-end receiver processor 24 is thecorrelation module 26. The primary purpose of the correlation module 26is to perform coherent processing on the signals-of-interest and toobtain the set of basic measurements 35. The specific algorithms andmethods used for coherent processing will depend on the signal structureof the signals-of-interest and on the application. FIG. 25 illustrates ageneric correlation architecture used in single-input GPS receivers.Most all GPS receivers on the market today are single-input receivers.Existing multi-input GPS receivers require multi-element, multi-aperturearray antennas where 3-D attitude is determined via phase interferometrytechniques. Any number of designs can be implemented with thearchitecture illustrated in FIG. 25 including loosely-coupled,tightly-coupled and ultra-tightly (deeply) coupled GPS systems. Ingeneral, the correlation module coherently extracts unique channels ofinformation embedded within an input signal 31 a (S). For example, eachGPS satellite signal is assigned a unique pseudo-random noise (PRN) codesequence and can be separated from all other satellite signals bycoherently applying the PRN sequence to the input signal 31 a (S).Hence, as indicated by the ith signal channel 41 a in FIG. 25, the inputsignal 31 a (S) is split into multiple information channels i=0,1, . . ., s, corresponding to the number of visible satellites in the sky(s).

The signal processing of each information channel is identical andcomprises a carrier-tracking loop and a code-tracking loop. Carrierwipeoff (removal) is achieved by mixing/multiplying 42 the input signal31 a (S) with an in-phase (cosine) replica of the IF sinusoidal carriersignal 54 and applying a low-pass filter on the result, yielding acarrier-free in-phase signal 55 (I_(S)). A carrier-free quadrature-phase(sine) signal 56 (Q_(S)) is generated by applying a 90° phase-shift 43to the replica of the IF sinusoidal carrier signal 54 andmixing/multiplying 44 the result with the input signal 31 a (S).

In loosely coupled systems a numerically controlled oscillator (NCO) 38for the carrier-tracking loop is typically driven by the carrier-freein-phase signal 55 (I_(S)) and its complement, the carrier-freequadrature-phase signal 56 (Q_(S)). A code-generator 39 generates‘early’ 48 (E), ‘prompt’ 49 (P), and ‘late’ 50 (L) copies of the GPS PRNsequence/code Ĉ_(k,m), where k corresponds to the time epoch, andcorrelates them with the carrier-free in-phase signal 55 (I_(S)) andcarrier-free quadrature-phase signal 56 (Q_(S)), both of which containthe actual satellite PRN sequence C_(k). The index m=(−1, 0, 1) inĈ_(k,m), corresponds to early, prompt, or late correlation. The earlycorrelator sequence 48 usually leads the prompt sequence 49 by half achip while the late sequence 50 lags by half a chip. The actual numberof correlators and the magnitude of the lead/lag separation depend onthe available processing power. The ideal correlation function η_(k,m)is defined as:

$\begin{matrix}{{\eta_{k,m}\left( {ɛ_{k},\delta} \right)} = {{E\left\lbrack {{\hat{C}}_{k,m}C_{k}} \right\rbrack} = \left\{ \begin{matrix}{{1 - {{ɛ_{k} + {m\; \delta}}}},} & {{{ɛ_{k} + {m\; \delta}}} < 1} \\{0,} & {{otherwise},}\end{matrix} \right.}} & (9)\end{matrix}$

where δ is the correlator spacing in chips, and ∈_(k) is the code delay(phase) error in units of chips (time delay (τ_(k))).

The early, prompt, and late in-phase correlation process comprisesmultiplication/mixing 45, 46 and 47, and integration 40 a. The processof code correlation is sometimes called code wipeoff. In legacy GPSsignals the code is modulated by data bits. Once the date bits areknown, code wipeoff can be used to achieve data wipeoff. Thequadrature-phase correlation process is identical to its in-phasecomplement. The correlation process results in an in-phase early 35 a(I_(SE)), an in-phase prompt 35 b (I_(SP)), an in-phase late 35 c(I_(SL)), a quadrature-phase early 35 d (Q_(SE)), a quadrature-phaseprompt 35 e (Q_(SP)), and a quadrature-phase late 35 f (Q_(SL)) signal.The carrier-loop is in lock when the quadrature-phase prompt signal 35 e(Q_(SP)) is driven to zero and the in-phase prompt signal 35 b (I_(SP))is maximized or, equivalently, when tan⁻¹(Q_(SP)/I_(SP)) is driven tozero. Code tracking is achieved by balancing the early and latecorrelator outputs 35 a (I_(SE)) and 35 c (I_(SL)), i.e., by driving{tilde over (η)}_(k)=η_(k,1)−η_(k,−1), to zero.

The carrier NCO 38 is driven by a carrier-loop feedback signal 34 bwhile the code-generator NCO 39 is driven by a code-loop feedback signal34 a. The code-loop feedback signal 34 a results in a stable loop aslong as the code lead/lag is within half a chip of the actual PRNsequence. In loosely-coupled or tightly-coupled systems the carrier-loopfeedback signal 34 b is a variation of the arctangent of thequadrature-phase prompt 35 e (Q_(SP)) and in-phase prompt 35 b (I_(SP))signals, or tan⁻¹(Q_(SP)/I_(SP)). Similarly, the code-loop feedbacksignal 34 a is simply the difference between the in-phase early signal35 a (I_(SE)) and the in-phase late signal 35 c (I_(SL)), or {tilde over(η)}_(k)=η_(k,1)−η_(k,−1). While some tightly-coupled GPS/INS systemsmake use of Doppler aiding, most typical receiver carrier- andcode-tracking loops operate without any knowledge or benefit from theposition, velocity, and time estimate 6 a (PVT) obtained from thenavigation filter embedded within the back-end processor 25 a. Incontrast, the back-end processor 25 a of an ultra-tightly coupled systemfuses all available information to estimate the pseudo-range and thepseudo-range rate to the ith satellite. The pseudo-range is used as thecode-loop feedback signal 34 a, and the pseudo-range rate is used as thecarrier-loop feedback signal 34 b. The ultra-tightly coupled approachhas significant advantages in terms of robustness and resistance tojamming.

The coherent correlation architecture shown in FIG. 25 is relativelysimple and more complex designs with more correlators are possible butare subject to available processing power. As illustrated in FIG. 25 asingle-input GPS receiver with input signal 31 a (S) requires onecarrier NCO 38, one code generator NCO 39, two carrier mixers 42 and 44,and six correlators comprising six code mixers 45, 46, 47, 61, 62, 63,and six integrators 40 a, as well as all low-pass filtering associatedwith mixing and signal multiplication.

Although we have provided some background for coherent processing of GPSsignals, the specific implementation of the GPS correlation, acquisitionand tracking loops will depend on the specific application and is notrelevant here. In fact, methods for coherent correlation, acquisitionand tracking of GPS and GNSS signals are well known and documented.Furthermore, although the architecture for coherent processing shown inFIG. 25 is depicted in the time-domain, frequency-domain implementationsexist and are becoming more common with the availability of low-costchips specialized for parallel processing and discrete Fouriertransforms (DFT). However, the single-input GPS coherent correlationarchitecture is not sufficient for obtaining direct (monopulse) attitudemeasurements while simultaneously providing protection against broadbandand narrowband sources of interference.

Existing anti-jam systems use the weighted sum of signals from multipleantenna elements to generate a single interference-free input signal 31a (S) for the GPS receiver and are unable to obtain direct attitudemeasurements. Multiple-input GPS receivers that do exist requiremulti-aperture antennas to determine the antenna attitude. Moreover,although U.S. Pat. No. 5,461,387 describes an instrument capable ofdetermining the antenna attitude from GPS signals using a single-inputGPS receiver, it does so by using a non-monopulse (sequential)commutative circuit and multiplexing the Mode 1 and Mode 2 signals (seeFIG. 6 in U.S. Pat. No. 5,461,387). It is widely acknowledged by thoseskilled in the art of direction-finding that non-monopulse DF receivershave serious drawbacks and are susceptible to electronic countermeasures (ECM). Moreover, since the phase of the GPS signal is alwaysvarying (due to the relative motion between the antenna and thesatellite), this sequential approach will introduce significant relativephase errors making it difficult, if not impossible, to provide accurateangle-of-arrival measurements and therefore attitude. This is probablythe primary reason for the absence of any commercial products based onthe technology of U.S. Pat. No. 5,461,387. Furthermore, as previouslymentioned, U.S. Pat. No. 5,461,387 does not provide the ability toprotect against intentional and unintentional jamming whilesimultaneously obtaining attitude measurements.

As illustrated in FIG. 2, a radio-based navigation receiver using amulti-mode DF antenna must be capable accepting at least two (monopulse)digital feed signals 4 a and 4 b, and coherently processing at leastthree signals 29 a (M1), 30 a (M2), and 31 a (S). The Mode 1 signals 29a (M1) and Mode 2 signals 30 a (M2) are required for monopulse directionfinding and attitude determination, while the “interference free”primary navigation input signal 31 a (S) is required for position,velocity, and time estimation. Hence, it appears that for each satellitesignal the coherent correlation module 26 needs to contain at leastthree sets of the carrier- and code-tracking loops shown in FIG. 25,including three carrier NCOs 38, three code generator NCOs 39, and allassociated mixers and low-pass filters totaling 18 code mixers andintegrators, and six carrier mixers. Needless to say the computationalburden required for radio-based attitude determination with asingle-aperture multi-mode DF antenna appears to be significant.However, further investigation shows that it is possible to make somesignificant simplifications without any significant loss in performance.

A correlation architecture is shown in FIG. 26 where the signals 29 a(M1), 30 a (M2), and 31 a (S) are all driven by the same carrier-loopnumerically-controlled oscillator 38 and code-loop NCO 39. Since theprocess of “mixing” two RF/IF signals conserves the signal phase, thesame carrier NCO 38 can be used for carrier wipeoff on the signals 29 a(M1) and 30 a (M2), thereby preserving the relative phase between thetwo signals 29 a (M1) and 30 a (M2). In the architecture shown in FIG.26, the Mode 1 in-phase signal 57 (I₁), Mode 1 quadrature-phase signal58 (Q₁), the Mode 2 in-phase signal 59 (I₂) and the Mode 2quadrature-phase signal 60 (Q₂) are formed by mixing them with asinusoidal signal of the same carrier IF frequency and phase used forthe primary navigation input signal 31 a (S), thereby requiring only asingle carrier NCO 38 for each satellite signal. The minimum number ofdigital carrier mixers required per satellite is therefore 2(n+1) wherethe number of antenna modes is n. Another advantage of this singlecarrier NCO architecture is that the attitude solution will be robust tocarrier cycle slips. It is possible for cycle slips to occur in one modebut not the other in a system where each of the three input signals hasits own carrier NCO, thus causing unnecessary relative phase errors. Asingle-NCO solution will not exhibit this problem.

The early, prompt and late in-phase and quadrature-phase components ofall signals are constructed after carrier wipeoff by mixing them with acopy of the GPS PRN code sequence {tilde over (C)}_(k,m). At firstglance it appears that three sets of code-tracking loops and codegenerator NCOs 39 are necessary for each satellite signal: one for theinput signal 31 a (S), and two for the Mode 1 and Mode 2 signals 29 a(M1) and 30 a (M2). However, as shown in FIG. 26, the prompt codesequence 49 of the input signal 31 a (S) can be used to achievecode-wipeoff for the Mode 1 and Mode 2 signals 29 a (M1) and 30 a (M2),thereby requiring only 10 correlators and a single code-generator NCO 39per satellite. Hence, the minimum number of digital correlators requiredper satellite is 2(3+n). Moreover, there is no significant loss ofinformation during the correlation process and both the relative gainand the relative phase information between the Mode 1 and Mode 2 signals29 a (M1) and 30 a (M2) is preserved. Furthermore, since the carrier NCO38 and the code-generator NCO 39 are driven by feedback from the inputsignal 31 a (S), which is protected against broadband interference, theMode 1 and Mode 2 signals 29 a (M1) and 30 a (M2) indirectly benefitfrom the robustness of the input signal 31 a (S).

As indicated by the architecture for the ith signal channel block 41 inFIG. 26, each satellite signal is permitted to have its own “optimal”set of weights for interference suppression and frequency excision. Thisis because the interference suppression module is included within theith signal channel block 41. This is a highly versatile architecturesince the interference rejection algorithms can also be used forsatellite-dependent multipath mitigation. In fact, the satellite signalangle-of-arrival measurements can be used to detect and avoid multipathsignals. However, although the embodiment shown in FIG. 26 requires thefewest number of mixers and carrier- and code-loop NCOs (one pair persatellite), the required processing power may still be of some concern.As shown in FIG. 27, the digital mode-forming network 23, theinterference suppression module 21, and the frequency excision module 22can be moved outside the ith signal channel block 41 b to be satelliteindependent, thereby reducing the computational burden.

Although the receiver embodiments shown in FIGS. 2, 25, 26 and 27 aretargeted for GPS and code-division multiple access (CDMA) systems, theycan easily be modified for alternative communications technologiesincluding, but not limited to time-division multiple access (TDMA),frequency-division multiple access (FDMA), orthogonal frequency-divisionmultiplexing (OFDM), and ultra-wideband (UWB) systems.

Position, Velocity, Attitude, and Time (PVAT) Determination

As indicated by FIGS. 2, 26 and 27, the outputs of the coherentcorrelation process are integrated and handed off (integrate and dump)to the back-end processor 25. The input signal 31 a (S) results in atleast six “true” measurements per satellite: the in-phase early 35 a(I_(SE)), prompt 35 b (I_(SP)), and late 35 c (I_(SL)) signals, and thequadrature-phase early 35 d (Q_(SE)), prompt 35 e (Q_(SP)), and late 35f (Q_(SL)) signals. One additional pseudo-measurement that is useful isthe signal power, or

A ² =I _(SP) ² +Q _(SP) ².  (10)

These seven signals are used to determine the platform position,velocity and time. Methods of determining position, velocity and timefrom GPS signals are well known to those skilled in the art and will notbe reviewed here.

The two direction-finding modes will result in a total of fouradditional “true” measurements per satellite: a Mode 1 in-phase promptsignal 35 g (I_(1P)), a Mode 2 in-phase prompt signal 35 i (I_(2P)), aMode 1 quadrature-phase prompt signal 35 h (Q_(1P)), and a Mode 2quadrature-phase prompt 35 j signal (Q_(2P)). These four signals areused to construct the relative gain

$\begin{matrix}{{{{r_{21}\left( {\theta,\varphi} \right)}} = \frac{\sqrt{I_{2P}^{2} + Q_{2\; P}^{2}}}{\sqrt{I_{1P}^{2} + Q_{1P}^{2}}}},} & (11)\end{matrix}$

and relative phase

∠r ₂₁(θφ)=tan⁻¹(Q _(2P) ,I _(2P))−tan⁻¹(Q _(1P) ,I _(1P)),  (12)

between Mode 1 and Mode 2 and can be considered as measurements insteadof 35 g, 35 h, 35 i and 35 j. Hence, depending on the specificimplementation chosen, the front-end receiver processor 24 generates upto 11 measurements per satellite for use in navigation.

The relative phase and relative gain measurements are then used todetermine the angle-of-arrival (θ,φ) of the satellite signal and,therefore, the platform attitude. A lookup table and an optimizationalgorithm can be used to generate the AOA measurements (θ,φ) thatprovide the best match with the measured values |r₂₁(θ,φ)| and∠r₂₁(θ,φ). As shown in FIGS. 26 and 27, and briefly alluded to withEquation (8), the calibration signal 53 (δDMN) can be fed back from theback-end processor 25 to the digital mode-forming network to ensure thatthe Mode 1 and Mode 2 patterns are properly aligned about boresight forimproved angle-of-arrival accuracy.

FIGS. 14 and 15 illustrate the direction-finding performance of atwo-arm spiral antenna using the composite angle error (see FIG. 7) as ametric. Modern signal processing and estimation algorithms may also beused [Penno 2001]. In general, methods for estimating theangle-of-arrival from relative gain and relative phase measurements arewell known: [Bullock 1971, Deschamps 1971, Corzine 1990, Kennedy 1984,Mosko 1984, Lipsky 1987, and U.S. Pat. No. 7,577,464].

The full 3-D attitude, or roll (α), pitch (β) and yaw (γ), of a platformcan be determined by measuring the angle-of-arrival of two or more GPSsatellites. A single GPS satellite signal can provide 2-D attitudeinformation. Since the positions of the satellites are obtained throughstandard GPS signal processing techniques, and the platform position canbe estimated from four or more satellite signals, the attitude of theplatform can be determined by minimizing the distance between themeasured AOA vectors (a_(j)) and projections of the known line-of-sightvectors from the platform to the GPS satellites (r_(j)). This process isillustrated by FIG. 28 and is known as Wahba's Problem [Wahba 1965].

The objective of Wahba's Problem is to find the set of arguments (α, β,γ) that minimize the cost functional

$\begin{matrix}{{{J(T)} = {\frac{1}{2}{\sum\limits_{j = 1}^{N}{\frac{1}{\sigma_{j}^{2}}{{a_{j} - {{T\left( {\alpha,\beta,\gamma} \right)}r_{j}}}}^{2}}}}},} & (13)\end{matrix}$

or arg min J(T(α,β,γ)), where and T(α,β, γ) is the inertial referenceframe to antenna frame rotation matrix that is a function of the threeEuler angles (β, β, γ),

$\begin{matrix}{{a_{j} = \begin{bmatrix}{{\sin \left( {\hat{\theta}}_{j} \right)}{\cos \left( {\hat{\varphi}}_{j} \right)}} \\{{\sin \left( {\hat{\theta}}_{j} \right)}{\sin \left( {\hat{\varphi}}_{j} \right)}} \\{\cos \left( {\hat{\theta}}_{j} \right)}\end{bmatrix}}{and}} & (14) \\{\xi_{j} = {\begin{bmatrix}{\hat{\theta}}_{j} \\{\hat{\varphi}}_{j}\end{bmatrix} = {\begin{bmatrix}\theta_{j} \\\varphi_{j}\end{bmatrix} + \begin{bmatrix}n_{\theta_{j}} \\n_{\varphi_{j}}\end{bmatrix}}}} & (15)\end{matrix}$

is the noisy AOA measurement with errors that are assumed to bezero-mean Gaussian with some covariance R_(j) that is a function of theangle-of-arrival

$\begin{matrix}\begin{matrix}{{p\left( \xi_{j} \right)} = {p\left( {{\hat{\theta}}_{j},{\hat{\varphi}}_{j}} \right)}} \\{= {\frac{1}{2\pi {R_{j}}^{1/2}}\exp {\left\{ {{- {\frac{1}{2}\begin{bmatrix}{{\hat{\theta}}_{j} - \theta_{j}} \\{{\hat{\varphi}}_{j} - \varphi_{j}}\end{bmatrix}}^{T}}{R_{j}^{- 1}\begin{bmatrix}{{\hat{\theta}}_{j} - \theta_{j}} \\{{\hat{\varphi}}_{j} - \varphi_{j}}\end{bmatrix}}} \right\}.}}}\end{matrix} & (16)\end{matrix}$

If there were no errors, then the true relationships between the AOAvector (a_(j)), the line-of-sight vector (r_(j)), and the elevation andazimuth angles are:

$\begin{matrix}{{{\theta_{j}\left( {\alpha,\beta,\gamma} \right)} = {{{\cos^{- 1}\left( \frac{z_{j}^{A}}{a_{j}} \right)}\mspace{14mu} {and}\mspace{14mu} {\varphi_{j}\left( {\alpha,\beta,\gamma} \right)}} = {\tan^{- 1}\left( \frac{y_{j}^{A}}{x_{j}^{A}} \right)}}},} & (17)\end{matrix}$

where

a _(j) =[x _(j) ² y _(j) ² z _(j) ²]^(T) =T(α,β,γ)r _(j).  (18)

Wahba's problem may also be formulated as a maximum likelihoodestimation problem. In that case,

$\begin{matrix}{{\hat{\alpha}}_{ML},{\hat{\beta}}_{ML},{{\hat{\gamma}}_{ML} = {\arg {\min\limits_{\alpha,\beta,\gamma}{\sum\limits_{j = 1}^{N}\left\{ {{\log {R_{j}}} + {\begin{bmatrix}{{\hat{\theta}}_{j} - {\theta_{j}\left( {\alpha,\beta,\gamma} \right)}} \\{{\hat{\varphi}}_{j},{- {\varphi_{j}\left( {\alpha,\beta,\gamma} \right)}}}\end{bmatrix}}_{R_{j}^{- 1}}^{2}} \right\}}}}}} & (19)\end{matrix}$

may be solved as an optimization problem or by taking the derivativeswith respect to the Euler angles, setting the resulting equations tozero, and solving for the maximum likelihood estimates of the Eulerangles. There are well known and elegant iterative algorithms forsolving Wahba's Problem [Farrell 1966, Cohen 1996] and will not bereviewed here.

It should be noted that since the distance between the platform and anyGPS satellite is at least 20,000 km, the error in the platform positionwould have to be approximately 350 km before the attitude estimate wouldhave an error of one degree. In general, angle-of-arrival measurementerrors are more significant than errors in platform position.

FIG. 29 shows the attitude accuracy of a two-arm spiral antenna as afunction of the number of satellites. The signal-to-noise ratio assumedis 29 dB and corresponds to the minimum GPS SNR obtained with a clearline-of-sight over an integration interval of 50 ms, or 20 Hz. NominalGPS signal power levels are 3-5 dB higher. FIG. 29 illustrates that asmall two-arm spiral antenna can obtain roll and pitch measurements at20 Hz with an accuracy of approximately 1.2° (1-σ), and yaw (azimuth)accuracies of approximately 2.1° (1-σ). The mean number of satellitesused in obtaining the 3-D attitude solution is less than the maximumnumber allowed due to the fact that satellites near the horizon wereignored. Errors increase less than 0.5° as the maximum number ofsatellites decreases from twelve to six. Furthermore, although FIG. 29only goes down to two satellites, even a single satellite provides 2-Dattitude information, and 3-D attitude can be recovered by making use ofalternative sensors such as magnetometers.

Finally, the attitude measurements of the system are not necessarilydependent on GPS signals. The system permits the use of any availablesignal within the capabilities of its RF front-end for navigation,including GLONASS and GALILEO signals, as well as alternative signalsfrom pseudolites and beacons. Furthermore, it is possible to modify theembodiments shown herein to obtain the angle-of-arrival of emitters ofunknown position, like jammers, while simultaneously measuring theangle-of-arrival of GPS signals for attitude determination.

RF-to-Digital Front-End

In the embodiments shown in FIGS. 2, 26 and 27, the signals from theantenna feed ports 2 a and 2 b are down converted by an RF-to-IFsubsystem 27 and then sampled by an analog-to-digital converter 28 tocreate the stream of digital signals which can be converted to digitalbaseband input signals 4 a and 4 b using a digital down-converter.Hence, the RF-to-digital front-end 3 comprises the RF-to-IF subsystem 27and the ADC subsystem 28, an optional DDC, and provides a digitized formof the signals from the feed ports 2 a and 2 b. Ideally, each antennafeed signal will be synchronously down-converted using a common clockand common phased-locked loops in order to avoid introducing asymmetricgain or phase errors that will result in AOA measurement errors.

In an alternative embodiment shown in FIG. 30, the RF-to-digitalfront-end 3 includes an analog mode- and/or pattern-forming network 36.The type of mode—and/or pattern-forming network depends upon method ofdirection-finding used, e.g., amplitude-comparison, phase-comparison, oramplitude-phase comparison, and whether or not the DF system will bemonopulse or sequential. The mode-forming network and/or pattern-formingnetwork can be implemented in either RF, IF or baseband [Corzine 1990]and is followed by the analog-to-digital converter 28. For the case ofan analog mode-forming network, sampled signals 29 and 30 correspond todigital mode signals M1 and M2. If a pattern-forming network isimplemented (with three or more elements), then the correlationprocessing 26 must be modified to match to the type of direction-findingarchitecture implemented, such as amplitude-amplitude comparison.

Furthermore, most of the radio receiver and navigation processor 5components have been traditionally implemented with analog hardware.Hence, it is clear that the locations of the mode-forming network, theinterference suppression module, the frequency excision module relativeto the ADC subsystem 28 is not important to the overall design of thesystem in terms of functionality. Regardless of the exact implementationof the RF-to-digital front-end, special care must be taken to ensurethat gain and phase of each RF channel are carefully matched as close aspossible. Although variations between RF channels will not significantlydegrade the interference rejection capabilities of the system, theattitude or direction-finding capabilities will be directly impacted byany such variation.

Integration with Additional Navigation Sensors

As illustrated by FIGS. 1, 2, 26, 27 and 30, optional additional sensors7 such as gyroscopes, accelerometers, inclinometers, and magnetometerscan provide measurements 8 to the digital radio receiver and navigationprocessor 5 that can further assist in improving the accuracy androbustness of the PVAT estimate 6. As an illustrative example, FIG. 31shows how the low-frequency GPS-based attitude (GPS/A) measurementscomplement the high-frequency measurements of a low-cost MEMS gyro. Theangle power spectral density (PSD) characteristic of a low-cost MEMSgyro is shown in FIG. 31 as a diagonal line 65 cutting across the upperright region of the graph. The primary source of error for a MEMS gyrois its rate flicker noise (FN), sometimes referred to as its bias, andits rate white noise (RWN). The diagonal line 65 shown in FIG. 31represents the PSD characteristics of a gyro with a 500 deg/sec flickernoise floor and a 5 deg/root-hour rate angle walk. Gyros with thesenoise characteristics sell for approximately $30/axis (in 2007 U.S.dollars).

The GPS/A PSD is shown as a horizontal line 64 in FIG. 31 for a systemwith a measurement error of 1.2° (1-σ) at 20 Hz and represents theantenna angle white noise (AWN) density over a bandwidth of 40π rad/sec(20 Hz). The attitude measurement bandwidth of 20 Hz is represented as avertical line 66. An angle noise of 0.18° (1-σ) for an integratedGyro+GPS/A system is determined by the square root of the area under thecurve defined by the lines 64, 65, and 66. Current three-axis GPS/INSsystems that are capable of 0.18° (1-σ) attitude accuracy cost over$5000. In contrast, the estimated cost of a three-axis GPS/A systemintegrated with low-cost MEMS gyros is $500.

Another benefit to integrating the GPS/A sensor with an INS is the addedrobustness that can be achieved against interference. In GPS/INS systemsthe carrier- and code-tracking loop bandwidths will depend on the methodof GPS/INS coupling. In general, tightly-coupled GPS/INS systems haveloop bandwidths on the order of 12-18 Hz under low dynamic conditions.Ultra-tightly coupled systems on the other hand can have loop bandwidthsas low as 3 Hz under high dynamics. Since the signal-to-noise ratio ofthe system is inversely proportional to the loop bandwidth,ultra-tightly coupled systems will have at least 6 dB of additionalanti-jam GPS capability and 10-15 dB is common. This in addition to anyprotection already provided by the interference suppression module 21and the frequency excision module 22.

Integrated Navigation, Guidance and Control

As illustrated by FIGS. 1, 2, 30 and, more specifically, FIG. 32, thePVAT estimate 6 can be further improved by optionally embedding platformguidance and control processing 5 b into the digital receiver andnavigation processor 5 in a closed-loop feedback structure. When anavigation processor 5 a is integrated with said guidance and controlprocessing 5 b, platform control commands 10 a and platform actuatormeasurements 10 b can be fed back into a model of the platform dynamics5 c to provide a pseudo-measurement 8 b (Ub) of platform position andorientation. Since platform control signals are generated in response toguidance commands, the pseudo-measurement 8 b (Ub) of platform positionand orientation has the properties of a predictor. In other words, itanticipates the platform motion in response to commanded controlsignals. This capability can be useful not only coasting through periodswhere navigation signals are denied, but for detecting sensor andactuator faults as well as estimating external forces 37.

Spin-Stabilized Platforms

Spin stabilized platforms provide some unique challenges due to theirroll rates about their stability axis. As illustrated by FIG. 33, anantenna mounted on a spin-stabilized platform with its antenna boresightaligned with the platform spin axis will measure an approximatelyconstant elevation angle. However, the measured relative phase of thetwo antenna modes and, therefore, the measured azimuth angle, will bephase-modulated by the platform spin rate. This is because the Mode 1phase varies approximately linearly with azimuth (roll) angle, while theMode 0 phase remains approximately constant. Hence, we can observe theroll angle and roll rate of the vehicle without requiring an expensiveIMU.

FIG. 34 illustrates an architecture for demodulating the phase (andamplitude) imparted by the platform roll. In this approach, the rolldemodulation module 67 follows the digital mode-forming network 23 andattempts to remove (track) the phase and amplitude modulation due toroll. The roll demodulation module input signal for Mode i is given by:

M _(i)(θ₀,φ(t))=G _(i)(θ₀,φ(t))S ₀(θ₀,φ₀),  (20)

where S₀(θ₀,φ₀)=Ac(t)d(t)sin(ω₀+ψ₀) is the selected radio-frequencynavigation signal received at an azimuth φ₀ and elevation angle θ₀defined at some arbitrary time t=0, A is the received magnitude, c(t) isthe GPS PRN code, d(t) is the GPS data, ω₀ is the received carrierfrequency, and ψ₀ is the received carrier phase. We assume that theelevation angle remains approximately constant θ(t)=θ₀ (or is slowlyvarying), while the azimuth angle varies with time at an approximatelyconstant (or slowly varying) roll rate ρ: φ(t)=ρt+φ₀. The ‘initial’angles (θ₀, φ₀) are ‘fixed’ relative to the global coordinate frame,while the platform continues to rotate. The complex antenna Mode i gainis G_(i)(θ, φ). Ideally, the Mode i output of the roll demodulationmodule is:

M _(i)(θ₀,φ(t))= G _(i)(θ₀,φ(t))M _(i)(θ₀,φ(t))=G _(i)(θ₀,φ₀)S₀(θ₀,φ₀),  (21)

where the roll demodulation gain G _(i)(θ₀,φ(t)) is defined such that:

G _(i)(θ₀,φ(t))G _(i)(θ₀,φ(t)):=G _(i)(θ₀,φ₀).  (22)

Hence, the outputs of the roll demodulation module are simply the slowlyvarying (relative to the roll rate) antenna mode signals as if theplatform were not rotating and remains ‘fixed’.

Since we have a priori knowledge of the antenna patterns, the inversegain function G _(i)(θ,φ) is known as a function of elevation andazimuth angle. However, we do not know the initial elevation θ₀ orazimuth φ₀ angles, or the roll rate ρ. The current orientation can bedetermined once the initial elevation and azimuth angles and the rollrate are estimated. Since it varies slowly over time relative to theroll rate, the initial elevation angle is directly observable withrelative magnitude measurements of the two antenna modes.

The roll rate and, therefore, the initial azimuth angle, is observablethrough the receiver phase lock loop (PLL) and frequency lock loop(FLL). This fact is clear from the following equation:

S(θ₀,φ(t))=α₁ M ₁(θ₀,φ(t))+α₂ M ₂(θ₀,φ(t))≈Δ(θ₀,φ(t))S ₀(θ₀,φ₀),  (23)

where α₁ and α₂ are the complex weights use to generate the primarynavigation signal S(θ₀,φ(t)), and Δ(θ₀,φ(t)) is the effective complexgain applied to the selected radio-frequency navigation signalS₀(θ₀,φ₀). Ideally Δ(θ₀,φ(t)):=1. However, in practice, there will besome residual error due to the non-zero roll rate such thatarg(Δ(θ₀,φ(t)))≈Ψ₁(ρ)t+Ψ₀(θ₀,φ₀) and

$\begin{matrix}\begin{matrix}{{S\left( {\theta_{0},{\varphi (t)}} \right)} \approx {{{Ac}(t)}{d(t)}{\sin\left( {{\omega_{0}t} + \psi_{0} + {\arg \left( {\Delta \left( {\theta_{0},{\varphi (t)}} \right)} \right)}} \right.}}} \\{\approx {{{Ac}(t)}{d(t)}{{\sin \left( {{\omega_{0}t} + \psi_{0} + {{\Psi_{1}(\rho)}t} + {\Psi_{0}\left( {\theta_{0},\varphi_{0}} \right)}} \right)}.}}}\end{matrix} & (24)\end{matrix}$

Hence, the non-zero rotation rate of the antenna will effectively shiftthe received frequency by Ψ₁(ρ) and the received phase by Ψ₀(θ₀,φ₀). Thereceiver frequency and phase lock loops will drive these error terms tozero and standard estimation techniques such as a Kalman filter can beused to estimate the roil rate and, therefore, the initial azimuthangle. The estimated signal arrival angles ({circumflex over (θ)}₀,{circumflex over (φ)}₀) and the estimated roll rate ({circumflex over(ρ)}) can then be used to compute the demodulation gain G_(i)({circumflex over (θ)}₀,{circumflex over (φ)}₀−{circumflex over(ρ)}t). The demodulation feedback loop 68 implied by FIG. 34 isexplicitly illustrated by FIG. 35 for a system with two DF modes. Therelative gain and phase measurements between the two modes arerespectively represented by | M ₂₁| and ∠ M ₂₁. This 3-D attitudedetermination architecture is valid for any DF antenna that supports atleast two DF modes and that can be placed upon a spinning platform. FIG.36 illustrates the coordinate system described above for amulti-aperture DF antenna placed about the outer surface of a spinningplatform. The antenna coordinate frame is represented by the subscript‘A’, while the ‘fixed’ or ‘initial’ coordinate frame is represented bythe subscript ‘0’.Multi-Antenna Attitude Systems with Multi-Mode Single-Aperture Antennas

Yet another application of this technology is the use of an array ofmulti-mode single-aperture DF antennas for attitude determination. It iswell known that there is an integer ambiguity that needs to be resolvedwith multi-antenna GPS-based attitude systems. Unfortunately, the searchspace for this ambiguity gets significantly larger with longer baselineswhich are required for improved attitude accuracy. The advantage ofusing an array of multi-mode single-aperture DF antennas and receiversis that the integer ambiguity remains bounded and no worse than a singleantenna solution regardless of the length of the baseline separationbetween array elements. Hence, the attitude accuracy of the system canbe improved by increasing the baseline separation without any increasein the computational burden required for determining the integerambiguity.

Although the present invention has been described with respect to apreferred embodiment thereof, it will be obvious to those skilled in therelevant art that many modifications, additions and deletions may bemade therein without departing from the scope and spirit of theinvention as set forth in the following claims.

1. A single-aperture direction-finding antenna comprising: a. at leastone conductive driven element located above a conductive ground surface;b. a plurality of feed ports driving said at least one conductive drivenelement, wherein the feed ports and the driven element arerotationally-symmetric about a common center above said conductiveground surface and support at least two direction-finding antenna modeswhile sharing a single radiating aperture; and c. at least onerotationally-symmetric conductive member electrically connected to saidconductive ground surface at a predetermined distance from said commoncenter and extending away from the ground surface toward said at leastone conductive driven element while leaving a gap between said at leastone conductive driven element and said conductive member, wherebyazimuthal phase and magnitude variations of said antenna modes arereduced resulting in improved angle-of-arrival accuracy anddirection-finding performance over a hemisphere above said conductiveground surface.
 2. The direction-finding antenna of claim 1, whereinsaid at least one conductive driven element comprises spiral arms. 3.The direction-finding antenna of claim 1, wherein said conductive membercomprises a conductive wall located along an outer perimeter of said atleast one conductive driven element.
 4. The direction-finding antenna ofclaim 1, wherein said conductive member comprises a set of conductiveposts distributed about an outer perimeter of said at least oneconductive driven element.
 5. The direction-finding antenna of claim 1,wherein: a. said at least one conductive driven element comprises spiralarms; and b. said conductive member comprises: (1) a cylindricalconductive wall located along a circular perimeter with a radiusapproximately equal to an outer radius of the spiral arms having a wallheight less than the gap between the ground surface and the spiral arms;and (2) a set of conductive posts distributed evenly about thecircumference of said conductive wall wherein the posts are electricallyconnected to the wall and vertically extend to approximately the sameheight as the spiral arms.
 6. A method for determining angle of arrivalof received radio-frequency signals at a receiving single-aperturedirection-finding antenna, said method comprising: a. receivingradio-frequency signals via a plurality of feed ports for at least onerotationally-symmetric conductive driven element emanating from a commoncenter above a conductive ground surface, wherein said at least oneconductive driven element and the feed ports support at least twodirection-finding antenna modes while sharing a single radiatingaperture; b. providing at least one rotationally-symmetric conductivemember electrically connected to said conductive ground surface at apredetermined distance from said common center and extending away fromthe ground surface toward said at least one conductive driven elementwhile leaving a gap between said at least one conductive driven elementand said conductive member; and c. determining angle-of-arrival of thereceived radio-frequency signals over a hemisphere above said conductiveground surface.
 7. The method of claim 6, wherein said at least oneconductive driven element comprises spiral arms.
 8. The method of claim6, wherein said conductive member comprises a conductive wall locatedalong an outer perimeter of said at least one conductive driven element.9. The method of claim 6, wherein said conductive member comprises a setof conductive posts distributed about an outer perimeter of said atleast one conductive driven element.
 10. The method of claim 6, wherein:a. said at least one rotationally-symmetric conductive driven elementcomprises spiral arms; and b. said conductive member comprises: (1) acylindrical conductive wall located along a circular perimeter with aradius approximately equal to an outer radius of the spiral arms havinga wall height less than the gap between the ground plane and the spiralarms; and (2) a set of conductive posts distributed evenly about thecircumference of said conductive wall wherein the posts are electricallyconnected to the wall and vertically extend to approximately the sameheight as the spiral arms.